A committee of 11 member is to be formed from 8 males and 5 females. If m is the number of ways the…

A committee of 11 member is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:
  1. m=n=68
  2.  n= m –8
  3. m=n=78
  4.  m+n=68

Solution

m=(6M, 5F)+(7M, 4F)+(8M, 3F)

=C6 8×C5 5+C7 8×C4 5+C8 8×C3 5

=28×1+8×5+1×10=78

n=(3F, 8M)+(4F, 7M)+(5F, 6M)

=C3 5×C8 8+C4 5×C7 8+C5 5×C6 8

=10×1+5×8+1×28=78

Hence, m=n=78.

Asked in: JEE Main 2019 (09 Apr Shift 1)

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