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  • In how many ways can a Quality Analyst team of 11 members be made from 16 experts such that 5 mathematics experts must always be included in the team?O

In how many ways can a Quality Analyst team of 11 members be made from 16 experts such that 5 mathematics experts must always be included in the team?

Option: 1

460


Option: 2

462


Option: 3

4460


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 particular things always included is \mathrm{=^{n-k}C_{r-k}}

Since 5 mathematics experts must always be included in the Quality Analyst, the following is evident.

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

           \mathrm{=n-k=16-5=11}

  • 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{=^{11}C_{6}}

\mathrm{=\frac{11!}{6!}5!}

\mathrm{=462}

 

 

Posted by

Sanket Gandhi

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