Question

In how many ways can a panel of 5 students be selected from 8 kids if a particular student is to be compulsorily included?

Answer 1

Solution:

Panel of 5 students needs to be selected.

Out of 8 students there will be a selection of 5 students.

But, there is 1 student from those 8 students which is compulsorily included in that panel of 5 students.

Therefore, there are only 4 students left to be selected for the panel from those 7 students.

So, the number of ways in which students will get selected will be =>

$^{7} C_{4}$

$\frac{7!}{(7-4)! 4!}$

$\frac{7 * 6 * 5 * 4!}{3! 4!}$

$\frac{7 * 6 * 5 }{3!}$

$7 * 5$

$35$

And also we have only 1 way to select that particular student who needs to be in that panel compulsorily.

So,

1 * 35 = 35 ways

The total number of ways in which a panel of 5 students be selected from 8 kids if a particular student is to be compulsorily included is 35 ways.