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  • Fill in the Blanks A committee of 6 is to be chosen from 10 men and 7 women so as to contain at least 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee.

Fill in the Blanks  A committee of 6 is to be chosen from 10 men and 7 women so as to contain at least 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee.

[Hint: At least 3 men and 2 women: The number of ways = ^{10}C_3 \times ^7C_3 + ^{10}C_4 \times ^7C_2.
For 2 particular women to be always there: the number of ways = ^{10}C_4 + ^{10}C_3 \times^5C_1.
The total number of committees when two particular women are never together = Total – together.]

 

Answers (1)

Number of ways of forming a committee of 6 persons containing atleast 3 men and 2 women

= ^{10}C_3* ^7C_3+ ^{10}C_4* ^7C_2=120*35+210*21=8610

  Total number of committee when two particular women are never together

=Total number of ways-Number of ways when 2 particular women are together

= \left (^{10}C_3* ^7C_3+ ^{10}C_4* ^7C_2 \right )- \left (^{10}C_4+ ^{10}C_3* ^5C_1 \right )

= 4200+4410-(210+600)=7800

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