# 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.

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.
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Calculation:
Total number of people $=6+6=12$
All possible ways of dividing 12 people in to two groups with 6 people in each
$=\frac{12!}{6!6!}$
$=924$
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
$=\frac{6!}{3!3!}×\frac{6!}{3!3!}$
$=20×20$
$=400$
P(same number of men in each group) $=\frac{400}{924}$
$=0.4329$
Hence, the probability $=0.4329$
The probability of getting equal number of men in two groups $=0.4329$