Solve the problem.
-A game involves choosing 8 numbers from the numbers 1 through 13. In how many ways can this be done?
A) 1267
B) 1295
C) 51,891,840
D) 1287

Question

Quizplus · Accepted Answer

This problem can be solved using the combination formula, which is used when the order of selection does not matter. The formula for combinations is C(n, k) = n! / [k!(n - k)!], where n is the total number of items to choose from, k is the number of items to choose, and "!" denotes factorial, the product of all positive integers up to that number. Here, n = 13 (numbers 1 through 13) and k = 8 (choosing 8 numbers). Thus, the calculation is C(13, 8) = 13! / [8!(13 - 8)!] = 13! / (8!5!) = (13×12×11×10×9) / (5×4×3×2×1) = 1287.

Solve the Problem. -A Game Involves Choosing 8 Numbers from the Numbers 1