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Answer:
There are 2450 ways.
Step-by-step explanation:
We can pick first the 4 man, and then the 4 women. The configuration of men and women are independant with each other, so the total of possibilities is obtained by multiplying the total possibilities to pick 4 men and the total possibilities of picking 4 women.
To pick 4 men from a group of 8, the total number of possibilities is the amount of ways to pick 4 elements from a group of 8. This number is represented by the combinatorial number of 8 with 4
To pick 4 women from a group of 7, we need to count the total amount of ways to pick 4 elements from a group of 7. This is the combinatorial number of 8 with 7
Hence, the total amount of ways to pick 4 men and 4 women from a group of 8 men and 7 women is 70*35 = 2450.