## 111. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

## 112. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

## 113. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

## 114. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

## 115. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

## 116. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

## 117. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

## 118. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

## 119. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

## 120. 20 men handshake with each other without repetition. What is the total number of handshakes made?

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