Combinations
Tested in 9 real MPSC questions across 3 years (2016–2020). See it in context on the interactive Concept Graph →
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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.
2, 3, 5, 6, 7 आणि 9 या अंकांपासून 5 ने भाग जाणारी आणि कोणतीही अंक पुन्हा न येता, अशा तीन अंकी किती संख्या तयार होऊ शकतील ? How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated ?
A 3-digit number is divisible by 5 if its unit's digit is 5. Given digits: 2, 3, 5, 6, 7, 9. Unit place can only be filled by '5' (1 way). The remaining 2 places can be filled from the remaining 5 digits (2, 3, 6, 7, 9) in 5P2 = 5 * 4 = 20 ways. Total numbers = 1 * 20 = 20.
15 पुरुष व 7 महिला यांच्यामधून 10 सदस्यीय समिती गठीत करावयाची आहे. समितीत कमीतकमी 6 महिलांचा समावेश असेल अशी समिती किती प्रकारे तयार करता येईल ?
Total committee size = 10 members from 15 men and 7 women, with AT LEAST 6 women. Cases: 1) 6 women and 4 men: 7C6 * 15C4 = 7 * 1365 = 9555. 2) 7 women and 3 men: 7C7 * 15C3 = 1 * 455 = 455. Total ways = 9555 + 455 = 10010.