Example 18 - A committee of 3 persons is to be constituted from - Combination

Example 18 - Chapter 7 Class 11 Permutations and Combinations - Part 2

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Example, 18 A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women? We have to select a committee of 5 different person taken 3 at a time Here, n = 5 r = 3 The required number of ways = nCr = 5C3 = 5!/3!(5 −3)! = 5!/3!2! = (5 × 4 × 3!)/(3! ×(2 × 1)) = 5 × 2 = 10 ways Total 2 men and 3 women Committees would consist of 1 man and 2 women Now we have to select 1 man from 2 men So, n = 2 r = 1 Number of ways = 2C1 = 2!/1!(2 −1)! = 2!/1!1! = 2 Number of ways to select 1 man & 2 women = 2 × 3 = 6 ways

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.