Problema Solution
there are 7 shuffled question cards left in a game Kim has to pick 20 of them an answer them both correct way to win what is the greatest number of different pairs of question cards can she pick.
Total question cards 3 4 5 6 7
number of pairs 3 6 10 15
Answer provided by our tutors
There must be a typo on the text of the question. I presume Kim has to pick 2 (not 20) questions out of 7.
we need to find the number of 2-combinations from a set of 7 elements
C(n, k) = n!/(k!(n - k)!)
n = 7 and k = 2
C(7, 2) = 7!/(2!(7 - 2)!)
C(7, 2) = 21
the greatest number of different pairs of question cards is 21.