Question

You have 6 friends. How many ways are there to invite a different subset of two of these friends over for dinner on 4 successive nights?
(A friend might be invited more than once; just the subset of 2 friends must be different each night.) \

ANSWER: P(C(6,2)4)

Answer 1

Total no of possible sunsets of 2 friends out of 6 = C(6,2) = 15

(Selection of AB & BA are same, so Combination is used)

Now, among these 15 subsets of size 2, we need to choose 4 different sunsets for the 4 nights.
Now, (AB on 1^st night & CD on 2^nd night) and (CD on 1^st night & AB on 2^nd night) are two different ways, so permutation will be used. So total ways = P(15,4) = ​​​​​​​P(C(6,2),4) = 32760