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?

$\left(6\right)75600canbewrittenas{2}^{4}\times {3}^{3}\times {5}^{2}\times {7}^{1}\phantom{\rule{0ex}{0ex}}Nowthefactorisoftheform{2}^{m}\times {3}^{n}\times {5}^{o}\times {7}^{p}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Nowmcantakevaluesfrom0to4i.e5values\phantom{\rule{0ex}{0ex}}ncantakevaluesfrom0to3i.e4values\phantom{\rule{0ex}{0ex}}ocantakevaluesfrom0to2i.e3values\phantom{\rule{0ex}{0ex}}pcantakevaluesfrom0to1i.e2values\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Hencenumberofdifferentfactorsof75600=5\times 4\times 3\times 2=120$

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