## 91. A book-shelf can accommodate 6 books from left to right. If 10 identical books on each of the languages A,B,C and D are available, In how many ways can the book shelf be filled such that book on the same languages are not put adjacently.

## 92. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

## 93. If the letters of the word **SACHIN** are arranged in all possible ways and these words are written out as in dictionary, then the word **SACHIN** appears at serial number:

**SACHIN**are arranged in all possible ways and these words are written out as in dictionary, then the word

**SACHIN**appears at serial number:

## 94. In how many ways can 3 men and their wives be made stand in a line such that none of the 3 men stand in a position that is ahead of his wife?

## 95. In a cricket match if a batsman score 0, 1, 2, 3, 4 or 6 runs of a ball, then find the number or different sequences in which he can score exactly 30 runs of an over. Assume that an over consists of only 6 balls and there were no extra and no run outs.

## 96. In how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together?

## 97. How many numbers are there between 100 and 1000 such that at least one of their digits is 6?

## 98. A student is required to answer 6 out of 10 questions divided into two groups each containing 5 questions. He is not permitted to attempt more than 4 from each group. In how many ways can he make the choice?

## 99. While packing for a business trip Mr. Debashis has packed 3 pairs of shoes, 4 pants, 3 half-pants,6 shirts, 3 sweater and 2 jackets. The outfit is defined as consisting of a pair of shoes, a choice of "lower wear" (either a pant or a half-pant), a choice of "upper wear" (it could be a shirt or a sweater or both) and finally he may or may not choose to wear a jacket. How many different outfits are possible?

## 100. How many positive integers 'n' can be form using the digits 3, 4, 4, 5, 6, 6, 7 if we want 'n' to exceed 60,00,000?

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