MPSC Rajyaseva 2016 CSAT — Question 66

6 पुरुष व 5 महिला यांच्या गटातून 5 सदस्यीय समिती स्थापन करावयाची आहे. यातून 3 पुरुष व 2 महिला असतील अशी समिती किती प्रकारे तयार करता येईल ? / A five-member committee is to be formed from the group comprising of 6 men and 5 women. In how many different ways can the committee be formed with 3 men and 2 women ?

To form a committee of 3 men and 2 women from 6 men and 5 women, we use combinations. Ways to select 3 men out of 6 is 6C3 = 20. Ways to select 2 women out of 5 is 5C2 = 10. Total ways = 6C3 * 5C2 = 20 * 10 = 200.