Answer:
210 different combinations are possible.
Step-by-step explanation:
Given that we need to choose two men from five men. The number of possible cases would be [tex]$ 5 \choose {2} $[/tex] [tex]$ = {^5}\textrm{C}_{2} $[/tex]
Also, since we have to choose two men for the post from seven women.
We will have: [tex]$ 7 \choose 2 $[/tex] [tex]$ = {^7}\textrm{C}_{2} $[/tex]
Note that: [tex]$ = {^n}\textrm{C}_{r} = \frac{n!}{(r!(n - r)!)} $[/tex]
[tex]$ \therefore {^5}\textrm{C}_{2} = \frac{5!}{(2!(5 - 2)!)} $[/tex]
[tex]$ = \frac{5!}{2! . 3!} = \textbf{10} $[/tex]
Also, [tex]$ {^7}\textrm{C}_{2} = \frac{7!}{(2!(7 - 2)!)} $[/tex]
[tex]$ = \frac{7!}{2! . 5!} = \textbf{21} $[/tex]
Since, we need two men and two women, we multiply the results.
= 10 X 21 = 210 which is the required answer.
Hence, the answer.
