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Syllabus

The letters of the word 'RANDOM' are written in all possible ways and these words are written out as in a dictionary.Find the rank of the word 'RANDOM'?

1) there is no restriction

2) 3 particular books always stand together

3) 2 particular books must occupy the ends.

A COLLEG AWARDED 38 MEDALS IN FOOTBALL,15 IN BASKET BALL AND 20 IN Cricket .if these medals went to a total of 58 men and only 3 men got medals in all the three sports hw many received medals in exactly two of the sports? plz answer wid explaination

How can we prove the formula n+r-1Cr when r things are to be selected out of n type of things where each object may be repeated any no. of times? OR how can we justify this formula logically?

In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?

If there are 4 routes between Delhi and Mumbai. In how many different ways can a man go from Delhi to Mumbai and return , if for returning

(i) any of the routes is taken

(i) the same route is not taken .

In how many ways can 3 prizes be distributed among 4 boys, when: (i) no boy gets more than one prize? (ii) a boy may get any number of prizes? (iii) no boy gets all the prizes?

Which word of the dictionary is 'MANGO' ?

how many 4 letter words can be formed from the word MORADABAD?

a boy has 3 library tickets and 8 books are of his interest. Of these 8,he doesn't want to borrow maths part 2, unless maths part 1 is also borrowed? In how many ways can he choose the 3 books to be borrowed ?

what is 5p4

how many numbers greater than 1000000 can be formed by using the digits 1,2,0,2,4,2,4?

In how many ways can final 11 players be selected from 15 cricket players-

a) there is no restriction

b) one of them must be included

c) one of them who is in bad form must be always be excluded

d) twof them being leg spinners one and only one must be included.

(a) 3

(b) 7

(c) 8

(d) 10

if letters of word 'MOTHER' are written in all possible orders and these words are written out as in dictionary find the rank pof the word 'MOTHER'.

In how many ways can 5girls and 3 boys be seated in a row so that no two boys are together

Find the number of ways in which 5 boys and 5 girls be seated in a row so that

1) No 2 girls mays sit together

2) All girls sit together and all boys sit together.

3) all girls never sit together.

In how many ways, can the letters of the word PENCIL be arranged so that

1) N is always next to E

2) N and E are always together.

how many four letter word can be form using letter of word "INEFFECTIVE"

(i) 3 same 1 different

(ii) 2same of one kind , 2 same of other kind

(iii)2 same, 2distinct

(iv) All different

How many numbers are there between 100 to 1000 such that at least one of their digit is 7 ?

1. Find the number of permutations that can be had from the letters of the word 'OMEGA' such that

How many natural numbers not exceeding 4321 can be formed with the digits 1,2,3 and 4,if the digits can repeat?

The answer is 229.I just need the steps.

a bit is either 0 or 1,a byte is a sequence of 8 bits find,

(a) the number of bytes that can be formed

(b) the number of bytes that begin with 11 and ends with 11

(c) the number of bytes that begin with 11 and do not end with 11

(d) the number of bytes that begin with 11or end with11

A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?

The letters of the word ‘ZENITH’ are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word ‘ZENITH’?

A class consist of 40 girls & 60 boys. In how many ways a president , vice president , treasurer , secretary be chosen. If the treasurer must be a girl & secretary must be a boy and a student cannot hold more than one position.

in how many can the letters of the word'FAILURE' be arranged so that the consonants may occupy only odd positions

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:

(i) exactly 3 girls? (ii) atleast 3 girls? (iii) atmost 3 girls?

how can we find the rank of a word in the dictionary?

If there are 6 periods in each working day of a school, in how many ways can one arrange 5 subjects such that each subject is allowed at least one period?

while solving this problem why we write

^{6}P_{5}??????Convert the following products into Factorials:

i) 6.7.8.9.10 ii) 2.4.6.8.10

1.Find the number of ways in which a mixed double tennis game can be arranged between 10 players consisting of 6 men and 4 women

2. In a hockey tournament , a total of 153 matches were played. If each team played one match with every other team, find the total number of teams that participated in the tournament

Ans -196

How many different words beginning and ending with a consonant, can be made out of letters of the word ' EQUATION ' ?

THIS IS A QUESTION OF PERMUTATION AND COMBINATION AND NOT PROBABILITY

I know that by using the formulae :- TOTAL COMBINATION I.e 52C4 - COMBINATION OF NON FACE CARDS I.e 40C4 Gives us the answer But can we attempt the question by making 4 conditions I.e as written in question that there must be atleast 1 face card so conditions so formed will be :-

1 face card( 12C1) AND 3 non face card (40C3)

2 face card (12C2) AND 2 non face card ( 40C2)

3 face card (12C3) AND 1 non face card (40C1)

4 face cards (12C4) and no non face card

Am I attempting question in right way ? But I am not getting the correct answer .. Please HELP ME TO GET THE ANSWER FROM THE METHOD AS SUGGESTED BY ME ABOVE IF IT IS FLAWLESS . IF IT HAS ANY FLAW PLEASE PLEASE PLEASE EXPLAIN IN DETAIL

_{n}denote the number of triangles which can be formed using the vertices of a regular polygon of 'n' sides. If T_{n+1}-T_{n}=21, then 'n' equals -if

^{n}C_{r}- 1 = 36,^{n}C_{r}= 84 and^{n}C_{r+1 }= 126, then find^{ r}C_{2}.[

HINT: form eqn using^{n}Cr/^{n}C_{r+1}and^{n}C_{r}/^{n}C_{r-1}to find the value of r.]A polygon has 35 diagonals . Find the number of its sides .

( ans. 10 )

Q) The number of seven letter words that can be formed by using the letters of the word SUCCESS so that two C are together but no two S are together......

NEED HELP!.....PLS TELL ME HOW TO DO THIS WITH A step-by-step solution

In an examination hall there are four rows of chairs.Each row has eight chairs one behind the other.There are 2 classes sitting for the examination with 16 students in each class.It is desired that in each row,all students belong to the same class and that no 2 adjacent rows are allotted to the same class.In how many ways can these 32 students be seated ?

How many natural numbers less than 1000 can be formed from the digits 0,1,2,3,4,5 when a digit may be repeated any number of time?

A code signal uses digit-letter-digit combinations but 0 and 1 are not used for either digits or letters. How many code signals are possible?

In how many ways can the letters of the word PERMUTATIONS be arranged if the

(i) words start with P and end with S, (ii) vowels are all together,

(ii) there are always 4 letters between P and S?

In how many distinct permutations of the letter in "MISSISSIPPI" do the four I's not come together?

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

^{12}C_{x}=^{12}C_{x+4}.1.PROVE n! /(n-r)!=n(n-1)(n-2)...(n-r+1)

2. (n-r+1).n!(n-r+1)!=n!/(n-r)!

1) The number of different words that can be formed with 12 consonents and 5 vowels by taking 4 consonents and 3 vowels in each word is?

Eight guests have to be seated 4 on each side of a long rectangular tabel. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in which the sitting arrangements can be made is?

3) A question paper contains 6 questions, each having an alternative. The number of ways an examine can answer one or more questions is?

4)A candidate is required to answer 6 out of 12 questions which are divided into two groups containing 6 questions in each group. He is not permitted to attempt not more than four from any group. The number of choices are?

5) The results of 8 matches (win,loss or draw) are to be predicted. The number of different forecasts containing exactly 6 correct results is?

6)The number of different factors the number 75600 has is?

7)The number of ways a person can contribute to a fund out of 1 ten-rupee note, 1 five-rupee note, 1 two-rupee and 1 one rupee note is?

8)The number of ways in which 9 things can be divided into two groups containing 2,3 and 4 things respectively is?

9) The number of even numbers greater than 300 can be formed with digits 1,2,3,4,5 without repetition is?

10)5 letters are written and there are five letter-boxes. The number of ways the letters can be dropped into the boxes, are in each?

^{n}C_{7 }=^{n}C_{9}, find the value of "n"^{n}C_{n-4 = 15, find "n"}^{28}C_{2r}:^{24}C_{2r-4}= 225 : 11 , find r. pls solve it soon thank ew......prove that 33! is divisible by 2^15.what is the largest integer n such that 33! is divisible by 2^n?

(1) 1880 (2) 1120 (3) 1240 (4) 1960

In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?

^{10}P_{r}= 720.## How many numbers are there between 99 and 1000 having

2.exactly one of their digits 71.at least one of their digits 7

in how many ways can the letters of the word ALGEBRA be arranged without changing the relative order of the vowels and consonants?

Pl ans Q4 (multi answer type)

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.

^{m+n}P_{2 }=90 AND^{m-n}P_{2}=30if all the letters of the word AGAIN bre arranged as in a dictonary, What is the 50th word?

^{nppppp}how many numbers greater than 1000,but not greater than 4000 can be formed with digits 0,1,2,3,4 if:i)Repetition of digits is allowed? ii)Repetition og digits is not allowed?

FIND r if:-

5 p

_{r}= 2^{6}p_{r-1}A} 3.75 days

B}4 days

C} 5 days

D}6 days

find the number of ways in which 5 ladies and 5 gentlemen may be seated in a row so that no two ladies are together.

In this problem why we use 11 places although there are only 10 persons?A cricket team of 11 players is to be chosen from 16 players which includes 5 bowlers and 2 wicket keepers. How many ways can a team be selected if each team must have 3 bowlers and 1 wicket keeper?? Plzzz answer!!

a puzzle has 8 empty spaces,each to be filled by the word YES or NO .In how many ways can it be solved ?

the letter of the worde SURITI are written in all possible orders and these words are written out as in dictionary.find the rank of the word suriti.

find the value of n, if n! / (n - 2 )! = 930 , n =4 .

ans : 31

if tanx =b/a , then what is the value of acos2x+bsin2x ?

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part

Iand PartII, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?if

^{n}p_{4}=360 than find nthere are 6 periods in each working day of school. in how many ways can 1 arrange 5 subjects such that each subject is allowed at least one period?

18 guest have to be seated half on each side of a long table. 4 particular guests desired to sit on one particular side & 3 others on the other side. Determine the no. of ways.

^{n}C_{r}*^{r}C_{p}=^{n}C_{p}*^{n-p}C_{r-p}