Question

Out of 9 people waiting for their turns for an interview, in how many ways can a selection for 4 be made if 1 particular person is always selected?

Answer 1

1 person is always selected.
so we are to select remaining 2 more
since 1 is already selected so total remaining 8
so we will select 3 out of 8
8C3

= 8 * 7 * 6 / ( 3 * 2)
= 56

56 ways.

thanks

Answer 2

Number of ways in which 4 candidates can be selected for the out of 9 candidates when a particular candidate is always selected is 56

Step-by-step explanation:

Number of people waiting for an interview = 9

Number of people to be selected = 4

If a particular person is always selected then we simply select the person and then rest 3 candidates have to be selected from the remaining 8 candidates

Therefore total ways in which 3 candidates are selected out of 9 candidates

$=^{8}C_3$

$=\frac{8!}{5!3!}$

$=\frac{8\times 7\times 6\times 5!}{5!\times 3\times 2}$

$=56$ ways

Therefore, there are 56 ways in which 4 candidates can be selected for the out of 9 candidates when a particular candidate is always selected.

Hope this answer is helpful.

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