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Q #6
:

In a box there are 90 slips numbered from 1 to 90. Ramu picks up four slips at random one after the other without replacement. What is the probability that the numbers on the slips in the order he has picked up is ascending?

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Since the slips are picked up one after the other without replacement, they have distinct numbers on them 4 distinct numbers can be arranged among themselves in 4! ways. (i.e. 24 ways). Of these 24 ways only one arrangement is in ascending order.

    ∴ The required probability = 1/24.


Q #7
:

In the land of ID, chess is always played by three players at a time. In a certain tournament, three persons played ten games of chess. In every game the winner, the first runner up and the second runner up get 5, 3 and 2 points respectively and in case of a draw everyone gets 2 points each. If after the tournament was over, the total number of points of all three participants put together was 92, how many drawn games were there?

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Assume that there are no draws to begin with Total points after 10 games = (5 + 3 + 2) x 10 = 100. But with each draw total falls by
(5 + 3 + 2) – (2 x 3) = 4 points.

    ∴we need (100 – 92) + 4 = draws.

 


Q #8
:

Anil and Sunil were practicing combinatorics as they were going home in their school van. There were 6 children in all in the van and the van was scheduled to make a total of 3 stops. Anil and Sunil, individually, calculated the number of ways for the students to get off. Unlike Anil, Sunil considers only the number of children who get off at each stop i.e. he does not distinguish between the students. Find the difference in the results obtained by the two.

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Q #9
:

Jeevan Blood Bank looks for three types of antigens in blood tests : A, B and Rh. When the antigen A or B is present, it is listed, but if both these are absent, the blood is type O. If the Rh antigen is present, the blood is positive, otherwise, it is negative. A laboratory technician reports the following results after testing the blood samples of 100 people.

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Using the Venn diagram   

    People who are O-ve = 100 – n (ABRh)

    =100 – [40 + 18 + 82 – 5 – 31 – 11 + 4]

    =100 – 97

    = 3


Q #10
:

Jeevan Blood Bank looks for three types of antigens in blood tests : A, B and Rh. When the antigen A or B is present, it is listed, but if both these are absent, the blood is type O. If the Rh antigen is present, the blood is positive, otherwise, it is negative. A laboratory technician reports the following results after testing the blood samples of 100 people. Find the no. of O+ people

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Using Venn diagram People who are O +ve = people who have only Rh = 44)