# 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?

i) possible nos. for the 1st(thousands) place are 1,2,3.

then no. of nos. can b formed = 3*5 *5*5

ii) ans. = 3*4*3*2

• -1
Ishika soni If repitition is not allowed , you have counted 375 but that also counts "1000" so correct answer should be 374 according to me . But the answer that i saw was also 375😊😊 ... ...
• 19
sidharth if repetation is not allowed then 1000 is not come but in this 4000 is not involved so 1000 is subtracted but 4000 is added so answer becomes 375 so this is coerrect

• -8
i hope this will help • 30
idk
• -11
Shivam if we will add all the possibilities then 125+125+125+1=376 The last one of 4 has left by u But the ans is 375
• 7
I too think that 374 should be the answer because if repetition is allowed then 1000 will too be there. So the answer should be 375-1=374. But that's not in the option.
• 0
I have the same question in my objective material. But as said by the mates above, in the case of repetition even i think that 1000 is included and thus that one outcome obtained at the last has to be subtracted from 375. The answer in our material says 374 and i think it actually makes sense. Its also given in the previous AIEEE 2002 paper. You can check that solution too...

Regards
Dharani
• -2
374 is correct answer but in every site answer given is 375 🙄
• 2
when repetition is allowed:
(i) numbers starting with 1 :
_     _    _   _
1  x 5 x 5  x 5= 125 , but this includes 1000 as well . As per the question 1000 is not to be included so the total number of numbers starting with 1 = 125-1=124
(ii) numbers starting with 2:
_    _    _   _
1 x 5 x 5 x 5=125 ways
(iii)numbers starting with 3 :
_    _    _   _
1 x 5 x 5 x 5=125 ways
In the question it states that " but not greater than 4000" which means we take 4001 onwards but we can take the numbers less than or equal to 4000....4000 is allowed as the question states greater than 4000 is not allowed but it never said 4000 itself is not allowed
so numbers starting with 4 = 1 ( which is 4000)