There are three rooms in a motel: one single, one double, and one for four persons. How many ways are there to house seven persons in these rooms?
7! / 1! 2! 3!
7!
7! / 3
7! / 3!
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1
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Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done
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10
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A coin is tossed 5 times. What is the probability that head appears an odd number of times?
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2
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In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
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3
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The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is
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4
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From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
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5
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A basketball team of 5 players is to be selected from a group of 10 men and 8 women players. A volley ball team of 6 players is to be selected from a group of 8 men and 7 women players. Find the difference in the number of ways in which both the teams are selected, given that each team has only 2 female players.
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6
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In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together
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7
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In how many ways the letters of the word “UNDERDOG” can be arranged such that the first and last letters are same and no two vowels are together?
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8
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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?
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9
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A committee of 8 members is to be selected from a group of 12 male and 10 female members. In how many ways the committee is selected such that at most two and at least one male member are there in the committee?
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