Answer :

Given that we need to select 7 members out of 9 boys and 4 girls by following the conditions:


i. exactly 3 girls


ii. at least 3 girls


iii. at most 3 girls.


It is told we need to select 7 members out of 9 boys and 4 girls with at least 3 girls.


The possible cases are the following:


i. Selecting 3 girls and 4 boys


ii. Selecting 4 girls and 3 boys


Let us assume the no. of ways of selecting is N1.


N1 = ((no. of ways of selecting 3 girls out of 4 girls) × (no. of ways of selecting 4 boys out of 9 boys)) × ((no. of ways of selecting 4 girls out of 4 girls) × (no. of ways of selecting 3 boys out of 9 boys))


N1 = ((4C3) × (9C4)) + ((4C4) × (9C3))


We know that ,


And also n! = (n)(n – 1)......2.1





N1 = (4 × 126) + (1 × 84)


N1 = 504 + 84


N1 = 588


The no. of ways of selecting 7 members with at least 3 girls is 588.


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