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# Permutations & Combinations

1.

In how many ways can the letters of the word ENCYCLOPAEDIA be arranged such that vowels only occupy the even positions?

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2.

In a question paper, there are four multiple choice type questions, each question has five choices with only one choice for it’s correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

Multiple choice type questions = 1 2 3 4

Total number of ways = 5x5x5x5 =625.

A number of correct answer = 1.

Number of false answers = 625-1 =624.

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3.

The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.

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4.

A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?

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5.

Number of circular permutations of different things taken all at a time is n!.

The number of circular permutations of different things taken all at a time is n-1! and the number of linear permutations of different things taken all at a time is n!.

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6.

If  Suraj doesn’t want three vowels together, then in how many, can he arrange letters of the word 'MARKER'?

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7.

A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is

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8.

How many words can be formed  by using all letters of word ALIVE.

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9.

In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?

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10.

In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?