Problema Solution
Keaton was playing jacks. In a particular round, he scattered six jacks on the floor. They were red, green, blue, yellow, purple, and orange. He picked up at least one of the jacks, and he might have picked up all six of them. How many possible combinations of jacks could he have picked up?
Answer provided by our tutors
C(n ,k) = n!/(k!(n - k)!)
C(6,1) + C(6, 2) + C(6, 3) + C(6, 4) + C(6, 5) + C(6, 6) =
= 6!/(5!1!) + 6!/(4!2!) + 6!/(3!3!) + 6!/(2!4!) + 6!/(1!5!) + 6!/(0!6!) =
= 6 + 15 + 20 + 15 + 6 + 1 = 63 possible combinations of jacks.