Combinations
Combinations is a Aptitude concept from the MPSC syllabus, tested in 9 past MPSC questions across 6 exam years between 2016 and 2025. Below are those real questions with their correct answers and explanations, plus the concepts worth being comfortable with first.
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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.
5 भाऊ आणि 3 बहिणींपैकी 1 बहिण आणि 2 भाऊ अशी तीन सदस्यांची समिती स्थापन करायची आहे. ते किती वेगवेगळ्या प्रकारे करता येऊ शकते? Out of 5 Brothers and 3 sisters, a committee of 3 members consisting of 1 sister and 2 brothers is to be formed. In how many different ways can it be done ?
Out of 5 brothers, 2 brothers are to be selected: 5C2 = 10. Out of 3 sisters, 1 sister is to be selected: 3C1 = 3. Total ways = 5C2 * 3C1 = 10 * 3 = 30.
3, 4, 7, 8, 9 या अंकांंच्या सहाय्याने कोणत्याही अंकाची पुनरावृत्ती न करता किती 2 अंकी संख्या बनवता येतील ? How many 2 digit numbers can be formed with the digits 3, 4, 7, 8, 9 if none of the digits is being repeated in any of the numbers so formed ?
To form a 2-digit number from 5 distinct digits (3, 4, 7, 8, 9) without repetition: Number of ways = 5P2 = 5 * 4 = 20.
3, 4, 5, 6, 7 यापैकी एकावेळी फक्त कोणतेही चार अंक एकदाच वापरून किती चार अंकी भिन्न संख्या तयार होतात ? Using any four digits at a time out of 3, 4, 5, 6, 7 only once, how many different numbers can be made ?
Using 5 distinct digits (3, 4, 5, 6, 7) to form 4-digit numbers where each digit is used only once: 5P4 = 5 * 4 * 3 * 2 = 120.