In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
120
720
4320
2160
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1
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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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2
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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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3
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There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?
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4
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Four letters are selected from the word “CAPAME” and are rearranged to form four letter words. How many words can be formed?
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5
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Ten participants are participating in a competition. In how many ways can the first three prizes be won?
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6
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A, B, C, D and E sit on five chairs all of which are facing north. C will sit only on the leftmost chair and B will not sit anywhere to the left of A. In how many ways they can be seated?
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7
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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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8
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How many integers between 1000 and 10000 have no digits other than 4, 5, or 6?
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9
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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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10
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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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