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

Solution:

We know that the number of ways of selecting r different things from n different things is a combination and is calculated using the formula ⁿCᵣ = n! / [r!(n−r)!].

Given that there are 6 red balls, 5 white balls, and 5 blue balls. 3 balls of each color should be selected.

• No. of ways of selecting 3 red balls out of 6 red balls = ⁶C₃
• No. of ways of selecting 3 white balls out of 5 white balls = ⁵C₃
• No. of ways of selecting 3 blue balls out of 5 blue balls = ⁵C₃

By fundamental principle of counting,

The required number of ways

= ⁶C₃ × ⁵C₃ × ⁵C₃

= (6!) / [3! (6-3)!] × (5!) / [3! (5-3)!] × (5!) / [3! (5-3)!] (Using nCr formula)

= 2000

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.4 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

Summary:

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 color is 2000