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Home » A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of (i)exactly 3 girls? (ii)at least 3 girls? (iii)at most 3 girls?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of
(i)exactly 3 girls?
(ii)at least 3 girls?
(iii)at most 3 girls?
Rs aggarwal Maths CBSE Class 11 Chapter 9 Exercise 9B
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of
(i)exactly 3 girls?
(ii)at least 3 girls?
(iii)at most 3 girls?

Answer : A committee of 7 has to be formed from 9 boys and 4 girls.

  1. Exactly 3 girls: If there are exactly 3 girls in the committee, then there must be 4 boys, and the ways in which they can be chosen is

= 504 ways= 4C3      9C4

  1. At least 3 girls: Here the possibilities are
  • 3 girls and 4 boys and
  • 4 girls and 3

The number of ways they can be selected

= 588= 4C3X9C4 + 4C4 X9C3

  • At most 3 girls:
  • 7 boys but no girls
  • 6 boys and 1 girl
  • 5 boys and 2 girls &
  • 4 boys and 3

And the number of their selection is

= 4C3 X9C4 + 4C2 X9C5 + 4C1 X9C6 + 4C0 X9C7

= 1584 ways.

 

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