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  • 18 civil engineers and 20 electrical engineers are nominated for the final round of the inter college debate completion. But 2 among them cannot join as they are hospitalized. In how many

18 civil engineers and 20 electrical engineers are nominated for the final round of the inter college debate completion. But 2 among them cannot join as they are hospitalized. In how many ways can the team of 15 head count be made now?

Option: 1

\frac{36!}{13!23!}


Option: 2

\frac{10!}{7!14!}


Option: 3

\frac{31!}{7!24!}


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

Since 2 engineers must never be included in the team, the following is evident.

  • The number from which the restricted combination is to be made is \mathrm{=n-k=\left ( 18+20 \right )-2=36} .

  • The number with which the restricted combination is to be made is \mathrm{=r-k=15-2=13}

Therefore, the required restricted combination is

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

\mathrm{=^{36}C_{13}}

=\frac{36!}{13!23!}

 

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