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In how many ways can a specialist team of 15 members be made from 26 men and 18 women such that no men are included and 3 female experts must always be included in the team?

Option: 1

460


Option: 2

462


Option: 3

4460


Option: 4

455


Answers (1)

best_answer

Note the following:

  • The formula for the combination for the selection of the \mathrm{x} items from the \mathrm{y}different items is \mathrm{=^{y}C_{x}=\frac{y!}{x!\left ( y-x \right )!}}

  • The restricted combination for the  selection of the \mathrm{r} items from the \mathrm{n} different items with \mathrm{k} particular things always included is \mathrm{=^{n-k}C_{r-k}}

Since 3 female experts must always be included in the specialist team, the following is evident.

  • The number from which the restricted combination is to be made is .

          \mathrm{=n-k=\left ( 26+18 \right )-\left ( 26+3 \right )=15}

  • The number with which the restricted combination is to be made is

         \mathrm{=r-k=\left ( 15+26 \right )-\left ( 3+26\right )=12}

Therefore, the required restricted combination is

\mathrm{=^{n-k}C_{r-k}}

\mathrm{=^{15}C_{12}}

=\frac{15!}{12!3!}

=455

 

Posted by

jitender.kumar

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