1. 12 applicants remain in the last phase of a scholarship application, where 5

Question

1. 12 applicants remain in the last phase of a scholarship application, where 5 of them are boys and 7 of them are girls. Mr. Lee plans to invite 3 boys and 4 girls for individual interviews next week, and thus he is going to make a list according to the ordering of interviews. Find the possible number of lists to be made according to each of the following conditions. (a) Select any 3 boys and 4 girls. (6) The boys should be interviewed successively. (c) Any two boys should not be interviewed successively.

Explanation / Answer

(A)

Number of ways of selecting 3 boys out of 5 and 4 girls out of 7 is

C(5,3)*C(7,4) = 350

(B)

Now three boys can arranged themselves in 3! ways and girls in 4! ways. Either boys can come first or last in the list so number of ways of making list is

350 * 3! *4! * 2 = 100800

(C)

The boys can arrange themseleves in 3! ways. There are two places between the boys so number of ways so selecting 2 girls out of 4 is C(4,2) = 6. These two girls can arrange themselves in 2! ways.

Rest 2 girls can be placed either start, end or middle of boys. So possible number of ways of arrangements is

3!*6 * 2! * 4*4 = 1152

So required number of ways is

1152 * 350 = 403200

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