In how many ways can a group of 10 men and 5 women be formed out of a total of 12 men and 10 women?

The number of ways to choose a group of 10 men from 12 men is given by the combination formula:

C(12,10) = 12! / (10! * 2!) = 66

Similarly, the number of ways to choose a group of 5 women from 10 women is given by:

C(10,5) = 10! / (5! * 5!) = 252

The total number of ways to form a group of 10 men and 5 women can be obtained by multiplying the number of ways to choose 10 men from 12 men by the number of ways to choose 5 women from 10 women, i.e.,

Total number of ways = 66 * 252 = 16,632

Therefore, there are 16,632 ways to form a group of 10 men and 5 women out of a total of 12 men and 10 women.