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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? - Mathematics

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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

\[= {}^4 C_1 \times^7 C_4 +^4 C_2 \times^7 C_3 + {}^4 C_3 \times^7 C_2 +^4 C_4 \times^7 C_1 \]
\[ = 140 + 210 + 84 + 7 \]
\[ = 441\]

Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 19.2 | Page 16

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