Question:
Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:
Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:
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To solve problems involving combinations, break down the selections into manageable cases and then sum the results for all valid combinations.
Updated On: Feb 5, 2026
- \( 8925 \)
- \( 8750 \)
- \( 9100 \)
- \( 8575 \)
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The Correct Option is B
Solution and Explanation
We need to choose 5 individuals from group A (which has 7 boys and 3 girls) and 3 individuals from group B (which has 6 boys and 5 girls).
For group A, we can select 3 boys and 2 girls, or 4 boys and 1 girl. The number of ways to select these members can be calculated using combinations:
\[
\text{Ways for group A} = \binom{7}{4} \times \binom{3}{1} + \binom{7}{3} \times \binom{3}{2}.
\]
For group B, we can select the remaining individuals:
\[
\text{Ways for group B} = \binom{6}{1} \times \binom{5}{2} + \binom{6}{2} \times \binom{5}{1}.
\]
Multiplying the total number of ways for both groups gives the final answer.
Final Answer: 8750.
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