Answer:
a) 13440
b) 4200
Step-by-step explanation:
a) The six people are different people. The possible combinations of couples from which the people are chosen is 10C6
For each choice of different couples either male or female, we have 2^6 possible outcomes.
So we have
(10C6) * 2^6
= (10! / (10-6)!6!) * 2^6
= (10! / 4!6!) * 2^6
= 210 * 2^6
= 13440
b) if the group has to have three men and three women, we choose the six different couples in 10C6 ways. From these six, there are 6C3 possibilities to choose from which couple to pick Female. From the rest we choose male.
We then have
(10C6)(6C3)
= (10!/ (10-6)!6!) * (6!/(6-3)!3!)
= (10!/4!6!) * (6!/3!3!)
= 210 * 20
= 4200
