the number of different 5-person committees that can be formed from 12 people is equal to the number of 5-combinations from a given set of 12 elements:

C(n , k) = n!/(k!(n-k)!))

n = 12 and k = 5

C(12, 5) = 12!/(5!(12-5)!)

C(12, 5) = 8*9*10*11*12/(2*3*4*5)

C(12, 5) = 782 committees can be formed.