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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1
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How many integers between 1000 and 10000 have no digits other than 4, 5, or 6?
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2
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How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?
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3
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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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4
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In how many ways can 10 people line up at a ticket window of a railway station?
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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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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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7
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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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8
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Three chairs are arranged in a row facing three other chairs. 4 boys and 2 girls are to be seated on these chairs such that girls are always facing each other. In how many ways can they be seated?
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9
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The students in a class are seated, according to their marks in the previous examination. Once, it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement, the teacher wants to write down all possible arrangements one in each of separate bits of paper in order to choose one of these by lots. How many bits of paper are required?
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10
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If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25 ?
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