Out of 8 men and 6 women working in an office, 9 are to be chosen for a meeting including at least 3 men and 2 women. Two men, who were present in the last meeting, have to attend this meeting. Find the number of ways in which they can be selected.
Explanation:
Out of 8 men and 6 women, 9 people have to be selected such that 2 men must attend and there has to be at least 3 men and 2 women.
Since 2 men must attend, now we need to select at least 1 more man and 2 women out of remaining 6 men and 6 women.
Case 1: 1 man + 6 women Number of ways = 6C1 × 6C6 = 6 × 1 = 6 ways
Case 2: 2 men + 5 women Number of ways = 6C2 × 6C5 = 15 × 6 = 90 ways
Case 3: 3 men + 4 women Number of ways = 6C3 × 6C4 = 20 × 15 = 300 ways
Case 4: 4 men + 3 women Number of ways = 6C4 × 6C3 = 15 × 20 = 300 ways
Case 5: 5 men + 2 women Number of ways = 6C5 × 6C2 = 6 × 15 = 90 ways
⇒ Total number of ways = 6 + 90 + 300 + 300 + 90 = 786.
Hence, option (d).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.