Since the order does not matter, it is a combination, also because they do not indicate how many men and how many women should be in the group of 8, which means that it would be the ways of putting together a group of 8 with 15 people (10 men + 5 women)
That is to say:
nCr = n! / (r! * (n-r)!)
n = 15, r = 8, replacing:
15C8 = 15! / (8! * (15-8)!)
15C8 = 6435
which means that there are 6435 ways to arm the group
