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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Three unbiased coins are tossed. What is the probability of getting at most two heads ?
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2
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A five-letter word is to be formed from a group of 5 vowels and 4 consonants, using at least one vowel and at least one consonant. In how many ways the word having a greater number of consonants than vowels can be formed?
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3
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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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4
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A biased coin in tossed thrice. What is the probability that heads turns out at least twice considering that the probability of a head is 60%?
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5
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Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
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6
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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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7
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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?
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8
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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least three men are in the committee. In how many ways can it be done?
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9
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In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
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10
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In how many ways can the letters of the word 'LEADER' be arranged?
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