Six boys and 4 girls are to be seated in two separate rows with five chairs each, such that two particular girls are always together and all the girls are not in the same row. In how many ways can they be seated?
15 * 7!
20 * 8!
18 * 7!
(16 * 8! – 4! * 6!)
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1
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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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2
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A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is
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3
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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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4
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One red flower, three white flowers, and two blue flowers are arranged in a line such that
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5
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A person tosses an unbiased coin. When head turns up, he gets Rs.8 and tail turns up he loses Rs.4. If 3 coins are tossed, what is probability that he gets a profit of Rs.12?
SolutionPerson will get profit of Rs 12 only when there is 2H (Head) and 1T (Tail) H + H + T = 12 8 + 8 + (-4) = 12 Total outcome of 2 head and 1 tail = 23 = 8 i.e (T, H, TH, HT, HH, HHT, HTH, THH) Total event with 2H and 1 T is 3 therfore probability = 3/8 |
6
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If a team of 4 persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least 1 female
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7
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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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8
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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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9
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There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?
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10
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Find the probability that a leap year selected at random will contain 53 Sundays
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