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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There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters.
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2
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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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3
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What is the sum of all 4 digit numbers that can be formed by the digits 1, 2, 3, 4 each exactly once
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4
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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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5
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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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6
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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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7
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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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8
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If (n + 2)! = 2550 (n!); find ’n’
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9
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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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10
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A box contains two white balls, three black balls and four red balls. Balls of the same colour are distinct. The number of ways in which three balls can be drawn from the box if atleast one black ball is to be included in the draw, is
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