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.

3. A blackout occurs if zero of the ten pairs are correct. If the group picks their pairs randomly, what is the probability of a single matchup ceremony being a blackout?

Explanation / Answer

No. of ways of first man picking a wrong woman = 9

Second man picking wrong woman = 8 and so on

Required porbabiltiy = 9!/10! = 1/10

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