Ex 7.4, 5 - Find number of ways of selecting 9 balls from 6 - Ex 7.4

  1. Chapter 7 Class 11 Permutations and Combinations
  2. Serial order wise
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Ex 7.4, 5 - Chapter 7 Class 11 Permutations and Combinations - NCERT Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour. We have to select 3 red balls from 6 red balls Here, n = 6 & r = 3 No of ways of selecting 3 red balls = 6C3 = 6!/3!(6 −3)! = 6!/3!3! = (6 × 5 × 4 × 3!)/(3! × 3 × 2) = (6 × 5 × 4 )/(3 × 2 ×1) = 20 We have to select 3 white balls from 5 white balls Here, n = 5 & r = 3 No of ways of selecting 3 white balls = 5C3 = 5!/3!(5 −3)! = 5!/3!2! = (5 × 4 × 3!)/(3! × 2 × 1) = (5 × 4)/2 = 10 We have to select 3 blue balls from 5 blue balls Here, n = 5 & r = 3 No of ways of selecting 3 white balls = 5C3 = 5!/3!(5 −3)! = 5!/3!2! = (5 × 4 × 3!)/(3! × 2 × 1) = (5 × 4)/2 = 10 The number of ways of selecting of 3 balls of each color = (No. of ways selecting 3 red balls) × (No. of ways selecting 3 white balls) × (no. of ways selecting 3 blue balls) = 20 × 10 × 10 = 2000

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