# Personnel selection. Suppose that 6 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 11 finalists, what is the probability of selecting (A) 3 females and 2​ males? ​(B) 4 females and 1​ male? ​(C) 5​ females?

Personnel selection. Suppose that 6 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 11 finalists, what is the probability of selecting
(A) 3 females and 2​ males?
​(B) 4 females and 1​ male?
​(C) 5​ females?
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Data analysis
Note : As per authoring guidelines, when multiple subparts are posted, then only first three subparts are to be answered.
Given there is selection for a Personnel.
And there are 11 finalists in which 6 are female and 5 are female.
And there are only 5 posts vacant.
To find the probability of selecting as below.
Total ways
Total number of ways of selecting 5 people from 11 finalists is given by,
$11P5$

$=55.440$
Probability is given by the ratio of number of favourable ways to the total number of ways.
Note :

A) 3 females and 2​ males
3 females selected from 6 female finalists in $6P3$ ways

$=120$
2 males selected from 5 male finalists in $5P2$ ways

$=20$
Favourable ways
Probability $=2400/55.440$
$=0.0432900433$
Hence probability of selecting 3 females and 2 males is 0.04329
(Rounded to 5 decimals)
B) 4 females and 1 males
4 females selected from 6 female finalists in $6P4$ ways

$=360$
1 male selected from 5 male finalists in $5P1$ ways
$=5$
Favourable ways
Probability $=1800/55.440$
$=0.0324675325$
Hence probability of selecting 4 females and 1 male is 0.0324675
(Rounded to 7 decimals)
C) 5 females
5 females selected from 6 female finalists in $6P5$ ways

$=720$
Favourable ways = 720
Probability $=720/55.440$
$=0.012987013$
Hence probability of selecting 5 females is 0.012987
(Rounded to 6 decimals)