How to find probability of forming an organisation with $3$ male students and $2$ female students if a particular male student must be included? There are $5$ male students and $6$ female students, $5$ students are needed to form an organisation.


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*Find the probability that $3$ male students and $2$ female students are members of the organisation, a certain male student must be a member of the organisation.


This is my steps (4C2 * 6C2)/10C4
Please help me

First, the number of ways to pick $3$ boys and $2$ girls from $5$ boys and $6$ girls respectively is:
($5$ choose $3$)($6$ choose $2$) = $(10)(15)$ = $150$ ways.
Next, the number of ways to pick $5$ students from the $11$ candidates (excluding the rule of a certain boy to be picked) is:
($11$ choose $5$) = $462$
However, we have to exclude the cases where all the members are girls. The number of ways to pick $5$ girls from $6$ is:
($6$ choose $5$) = $6$
Now, subtracting this from the initial number of total ways of picking random students is $462-6 = 456$ ways.
Hence, the probability that 3 male students and 2 female students are members of the organization given that a certain male student must be a member of the organization is:
$\frac{150}{456} = \frac{25}{76} ≈ 32.89$ %
