Question

Q.17
Out of 6 boys and 4 girls a group of 7 is to
be formed. How many such groups are
possible if boys are to be in majority?
(A) 120 (B) 90 (C) 100 (D) 80​

Answer 1

Answer:

number of boys and girls in the 7 member group can be:

4 boys 3 girls

5 boys 2 girls

6 boys 1 girl

you can't have more than 6 boys since that's all that is available.

3 boys in the 7 member group would not be a majority because you would then have 4 girls.

4 boys 3 girls is calculated as 6C4 * 4C3 = 15 * 4 = 60

5 boys 2 girls is calculated as 6C5 * 4C2 = 6 * 6 = 36

6 boys 1 girl is calculated as 6C6 * 4C1 = 1 * 4 = 4

add them up together and you get 100 possible ways that the group can be formed where the boys are in the majority.

Answer 2

Answer:

(C) 100 is the right answer.

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