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In how many ways can a cricket team be made from 10 girls of school A and 12 girls of school B, such that 5 special experts among them are always included in the team?

Option: 1

12376


Option: 2

12356


Option: 3

12346


Option: 4

Cannot be determined


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!(y-x)!}}

  • 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}}

As per the available data, the total number of the girls

=10+12=22

There are eleven members in a cricket team.

Since 5 special experts must always be included in the team, the following is evident.

  • The number from which the restricted combination is to be made is \mathrm{=n-k=22-5=17}

  • The number with which the restricted combination is to be made is \mathrm{=r-k=11-5=6}

Therefore, the required restricted combination is

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

\mathrm{=^{17}C_{6}}

=\frac{17!}{6!11!}

=12376

Posted by

Anam Khan

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