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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 (ii) at least one boy and one girl?
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Solution
If the team has at least 1 boy and 1 girl, then the number of ways of selecting 5 members
\[= {}^4 C_1 \times^7 C_4 +^4 C_2 \times^7 C_3 + {}^4 C_3 \times^7 C_2 +^4 C_4 \times^7 C_1 \]
\[ = 140 + 210 + 84 + 7 \]
\[ = 441\]
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