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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