Problema Solution
Carmen has nine buttons with funny sayings she would like to put some funny buttons on her backpack but there is room for only 2 what is the greatest number of different ways she can select two buttons to put on her backpack.
total number of buttons 3 4 5 6 7 8 9
number of ways 3 6 10 15
Answer provided by our tutors
we need to find the number of 2-combinations from a set of 9 elements
C(n, k) = n!/(k!(n - k)!)
n = 9 and k = 2
C(9, 2) = 9!/(2!(9 - 2)!)
C(9, 2) = 36
she can select two buttons out of 9 in 36 different ways.