A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

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)!]. Using this,

• No. of ways of selecting 2 black balls out of 5 black balls = ⁵C₂
• No. of ways of selecting 3 red balls out of 6 red balls = ⁶C₃

By fundamental principle of counting,

Required number of ways = ⁵C₂ × ⁶C₃

= (5!) / [2! (5-2)!] × (6!) / [3! (6-3)!]  (Using nCr formula)

= 10 × 20

= 200

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.4 Question 8

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

Summary:

No. of ways of selecting 2 black and 3 red balls from a bag of 5 black and 6 red balls is 200