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Home » A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways can this be done, when (i) at least 2 ladies are included? (ii) at most 2 ladies are included?
A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways can this be done, when (i) at least 2 ladies are included? (ii) at most 2 ladies are included?
Rs aggarwal Maths CBSE Class 11 Chapter 9 Exercise 9B
A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways can this be done, when (i) at least 2 ladies are included? (ii) at most 2 ladies are included?

Answer : Since the committee of 5 is to be formed from 6 gents and 4 ladies.

(i) Forming a committee with at least 2 ladies Here the possibilities are

  • 2 ladies and 3 gents
  • 3 ladies and 2 gents
  • 4 ladies and 1 gent

The number of ways they can be selected

= 186 ways= 4C2 X6C3 + 4C3X6C2 + 4C4X6C1

(ii) The number of ways in this case is

  1. 0 ladies and 5 gents
  2. 1 lady and 4 gents
  3. 2 ladies and 3

The total ways are

= 4C0 X6C5 + 4C1X6C4 + 4C2 X 6C3

= 186 ways.

 

i

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