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Question
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least one boy and one girl
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Solution
We have 4 girls and 7 boys and a team of 5 members is to be selected.
When at least one by and one girl are to be selected
Number of ways = 4C3 × 7C4 + 4C2 × 7C3 + 4C3 × 7C2 + 4C4 × 7C1
= `4 xx (7 xx 6 xx 5 xx 4)/(4 xx 3 xx 2 xx 1) + (4 xx 3)/(2 xx 1) xx (7 xx 6 xx 5)/(3 xx 2 xx 1) + 4 x (7 xx 6)/(2 xx 1) + 1 xx 7`
= 4 × 35 + 6 v 35 + 4 × 21 + 7
= 40 + 210 + 84 + 7
= 441 ways
Hence the required number of ways are 441 ways
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