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.

Answer 1

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 \(\displaystyle={0.4329}\)
Answer:
The probability of getting equal number of men in two groups \(\displaystyle={0.4329}\)