A college wishes to form a seven-member cultural committee from 8 distinct boys and 7…
MATHEMATICS · Subjective · CBSE · Mathematics · Permutations and Combinations · Permutations and Combinations
Problem
A college wishes to form a seven-member cultural committee from 8 distinct boys and 7 distinct girls. The committee must include
• at least 3 girls, and
• at most 4 boys.
(i) Obtain the number of possible committees by considering separately each admissible distribution of boys and girls that satisfies the above restrictions. Show all intermediate working.
(ii) Recalculate the answer by subtracting from the total number of possible seven-member committees the number of committees that violate at least one of the two given conditions. Hence verify that the two approaches give the same numerical result.