a group consists of 4 girls and 7 boys .in how many ways can a team of 5 members be selected in the team have at least one boy and one girl??
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Answer:
No.of ways of selecting a team of 5 members from 4 girls and 7 boys such that the team has atleast one boy and one girl can be divided into cases.
1) One boy and 4 girls
No.of ways = 7C1 * 4C4 = 7
2) Two boys and three girls
No.of ways = 7C2* 4c3 = 21*4 = 84
3) Three boys and two girls
No.of ways = 7C3 * 4C2
4) Four boys and one girl
No.of ways = 7C4* 4C1
So,
Total no.of ways = Sum of ways of each of these cases which is
= 7C1 * 4C4 + 7C2*4C3 + 7C3*4C2 + 7C4* 4C1
Hope this helps you !
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