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  • In how many ways can a captain reject the 10 underperformers from the team of 25 head count among whom 2 are injured and 3 are out of country?Option: 1

In how many ways can a captain reject the 10 underperformers from the team of 25 head count among whom 2 are injured and 3 are out of country?

Option: 1

1460


Option: 2

3003


Option: 3

4416


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!\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}}

As per the available data, the number of the underperformers who must always be present in the rejection list is

=2+3

=5

Since 5 members are confirmed to be rejected from the team, the following is evident.

  • The number from which the restricted combination is to be made is \mathrm{=n-k=25-10=15}.

  • The number with which the restricted combination is to be made is \mathrm{=r-k=10-5=5}

Therefore, the required restricted combination is

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

=\mathrm{^{15}C_{5}}

=\frac{15!}{10!15!}

=3003

 

 

 

Posted by

Rishabh

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