In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
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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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If A and B are two independent events with P(A) = 3/5 and P(B) = 4/9 , then P(A' ∩ B' ) equals
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3
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In a single throw with four dice,the probability of throwing seven is
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4
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A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?
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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 = 2^{3} = 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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One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is not a face card (Jack, Queen and King only)?
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7
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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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8
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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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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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The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is
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