Question # To find: The probability of getting same number of men in two groups. Given: A group consists of 6 men and 6 women. Divide into groups 6 in each.

Comparing two groups
ANSWERED To find: The probability of getting same number of men in two groups.
Given:
A group consists of 6 men and 6 women. Divide into groups 6 in each. 2021-01-31
Calculation:
Total number of people $$\displaystyle={6}+{6}={12}$$
All possible ways of dividing 12 people in to two groups with 6 people in each
$$\displaystyle={\frac{{{12}!}}{{{6}!{6}!}}}$$
$$\displaystyle={924}$$
If both groups are having same number of menm then each group consist 3 men and 3 women.
The possible ways of getting 3 men and 3 women in each group is
$$\displaystyle={\frac{{{6}!}}{{{3}!{3}!}}}\times{\frac{{{6}!}}{{{3}!{3}!}}}$$
$$\displaystyle={20}\times{20}$$
$$\displaystyle={400}$$
P(same number of men in each group) $$\displaystyle={\frac{{{400}}}{{{924}}}}$$
$$\displaystyle={0.4329}$$
Hence, the probability $$\displaystyle={0.4329}$$
The probability of getting equal number of men in two groups $$\displaystyle={0.4329}$$