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?
10
18
36
12
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A speaks truth in 75% cases and B in 80% of the cases. In what percentage of the cases are they likely to contradict each other, narrating the same incident?
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2
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There are 8 orators A, B, C, D, E, F, G, and H. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
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3
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It is required to seat 5 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
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4
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How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place?
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5
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If C(n, 7) = C(n, 5), find n
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6
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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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7
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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?
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8
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In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together
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9
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How many 5 digit even numbers with distinct digits can be formed using the digits 1, 2, 5, 5, 4?
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10
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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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