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In how many ways can Sheela form a musical team of 11 members from 20 head count such that 2 trained vocalists, 1 tabla player, 1 harmonium playerfrom them must always be included in the team?
Option: 1
$\frac{16!}{7!11!}$

Option: 2
$\frac{16!}{7!9!}$

Option: 3
$\frac{18!}{7!11!}$

Option: 4
$\frac{20!}{7!9!}$

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

The number of team members who must always be present in the team is

$=2+1+1$

$=4$

Since 4 musical experts must always be included in the team, the following is evident.

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

$\mathrm{n-k=20-4=16}$

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

$\mathrm{r-k=11-4=7}$

Therefore, the required restricted combination is

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

$\mathrm{=^{16}C_{7}}$

$=\frac{16!}{7!9!}$

Posted by

jitender.kumar

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