The television network MTV airs a show called “Are You The One?” Unlike many oth

Question

The television network MTV airs a show called “Are You The One?” Unlike many other TV shows on the network, the show features a surprising amount of mathematics. 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.

2. 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

Total no. of possibilites = 10! = 3628800

Probability of winning = 1/3628800

In the second case, A pair does not choose the same partner as before - Hence, total no. of ways = 9!= 362880

Probability of winning = 1/362880

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