Solve Counting Problems Using Combinations
-To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50.) The order in which the selections is made does not matter. How many different selections are possible
A) 15,890,700
B) 13,983,816
C) 300
D) 720

Question

Quizplus · Accepted Answer

The number of different selections is given by the combination formula:C(n, r) = n! / (n - r)! / r!where n is the total number of items and r is the number of items to be selected.In this case, n = 50 and r = 6, so the number of different selections is:C(50, 6) = 50! / (50 - 6)! / 6! = 15,890,700