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  • In how many ways can a medical team of 20 head count be made from 25 medical experts such that 2 eye specialists and 3 surgeons among them must always be present?<div class='qna-optio

In how many ways can a medical team of 20 head count be made from 25 medical experts such that 2 eye specialists and 3 surgeons among them must always be present?

Option: 1

11460


Option: 2

15504


Option: 3

44160


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{y}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 medical experts who must always be present is

=2+3

=5

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

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

          \mathrm{=n-k=25-5=20}.

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

          \mathrm{=r-k=20-5=15}

Therefore, the required restricted combination is

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

\mathrm{=^{20}C_{15}}

=\frac{20!}{15!5!}

=15504

 

 

Posted by

Devendra Khairwa

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