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In how many ways can a Quality Analyst team of 20 members be made from 6 Hindi experts, 5 English Experts, 16 Science experts and 15 other subjects’ experts among whom 5 experts are absent and 2 specified experts must always be included in the team?
Option: 1
$\frac{35!}{18!17!}$

Option: 2
$\frac{55!}{18!17!}$

Option: 3
$\frac{35!}{19!17!}$

Option: 4
Cannot be determined

Answers (1)

best_answer

Note the following:

The formula for the combination for the selection of the items $\mathrm{x}$ from the $\mathrm{y}$ different items is $\mathrm{=^{y}C_{x}=\frac{y!}{x!\left ( y-x \right )!}}$
The combination for the selection of the items $\mathrm{r}$ from the $\mathrm{n}$ different items with $\mathrm{k}$ particular things always included and $\mathrm{h}$ particular things always excluded is $\mathrm{^{n-k-h}C_{r-k}}$

Since 5 experts are absent and 2 specified experts must always be included in the Quality Analystteam, the following is evident.

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

$\mathrm{=n-k-h=(6+5+16+15)-2-5=42-7=35}$

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

$\mathrm{=r-k=20-2=18}$

Therefore, the required restricted combination is

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

$\mathrm{=^{35}C_{18}}$

$\mathrm{=\frac{35!}{18!17!}}$

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Anam Khan

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