## 41. There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?

## 42. Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.

## 43. In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?

## 44. There are three prizes to be distributed among five students. If no students gets more than one prize, then this can be done in:

## 45. A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?

## 46. A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is:

## 47. If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

## 48. In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?

## 49. What is the value of 1 × 1! + 2 × 2! + 3 × 3! + . . . . . . . . n × n!

where n! means n factorial or n(n-1) (n-2) . . . . . . . . 1

where n! means n factorial or n(n-1) (n-2) . . . . . . . . 1

## 50. When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?

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