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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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?
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2
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From a pack of 52 playing cards, two cards are drawn together at random. Calculate the probability of both the cards being the Kings.
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3
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How many four-digit numbers, each divisible by 4 can be formed using the digits 5, 6, 7, 8, 9, repetition of digits being allowed in any number?
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4
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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?
Solution |
5
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How many integers between 1000 and 10000 have no digits other than 4, 5, or 6?
Solution |
6
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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.
Solution |
7
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Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Solution |
8
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Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?
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9
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A number lock on a suitcase has 3 wheels each labeled with 10 digits from 0 to 9. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
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10
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Three unbiased coins are tossed. What is the probability of getting at most two heads ?
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