Question 5 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.
Class X1 - Maths -Permutations and Combinations Page 153
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total number of red balls = 6
total number of white balls = 5
total number of blue balls = 5
now,
3 red balls out of 6 red balls can be selected in ⁶C₃ ways .
3 white balls out of 5 white balls can be selected in ⁵C₃ ways .
3 blue balls out of 5 blue balls can be selected in ⁵C₃ ways .
now, A/C to fundamental principal of counting,
total number of ways selecting 9 balls (3 balls of each colors ) is
= ⁶C₃ × ⁵C₃ × ⁵C₃
= 6!/3!×3! × 5!/3!×2! × 5!/3!×2!
= (6 × 5 × 4/6 ) × ( 5 × 4/2) × (5 × 4/2)
= 20 × 10 × 10
= 2000 ways .
total number of white balls = 5
total number of blue balls = 5
now,
3 red balls out of 6 red balls can be selected in ⁶C₃ ways .
3 white balls out of 5 white balls can be selected in ⁵C₃ ways .
3 blue balls out of 5 blue balls can be selected in ⁵C₃ ways .
now, A/C to fundamental principal of counting,
total number of ways selecting 9 balls (3 balls of each colors ) is
= ⁶C₃ × ⁵C₃ × ⁵C₃
= 6!/3!×3! × 5!/3!×2! × 5!/3!×2!
= (6 × 5 × 4/6 ) × ( 5 × 4/2) × (5 × 4/2)
= 20 × 10 × 10
= 2000 ways .
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