The television network MTV airs a show called “Are You The One?”The premise of t

Question

The television network MTV airs a show called “Are You The One?”The premise of the show is that ten men and ten women live in a house together. Secretly, the group has been split into ten“ correct” male-female pairs which a matchmaker believes to be especially compatible. In other words, each player has exactly one “perfect match” of the opposite sex, though they have no idea which other player is their perfect match. A matchup ceremony happens at the end of each episode, in which the group of twenty players partition themselves into ten male-female pairs. The players are not told whether or not their specific matches are correct, they are only told how many pairs are correct.

1. The group wins if they get all ten pairs right at a single matchup ceremony. They have ten matchup ceremonies in which to do so. What is the probability that the group wins? First assume that the players are bad strategists, and may accidentally repeat a matchup ceremony. Then solve the problem again assuming the players are good strategists, and are therefore unwilling to repeat a matchup ceremony exactly.

Explanation / Answer

The required probability is P(first partner choses his perfect match amoung 5 people)*P(second partner choses his perfect match amoung 4 other people)*P(third partner choses his perfect match amoung 3 people)*P(fourth partner choses his perfect match amoung remaining 2 people)*P(fifth partner choses his perfect match amoung remaining 1 person)

= 1/5 * 1/4 * 1/3 * 1/2 *1

=1/120

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