A young man has 4 girlfriends A, B, C, D One night he wrote a love letter to eac

Question

A young man has 4 girlfriends

A, B, C, D

One night he wrote a love letter to each of the girls, and addressed 4 envelopes. But before he puts the letters in the correct envelopes, there is a power outage and he just puts the letters in the envelopes at random.

a.) How many ways can the 4 letters go into 4 envelopes?

4 choices*3choices*2choices*1choice = 4! =24 ways

b.) How many ways can all of the letters go to the wrong envelope, and compute the probability that the toung man will lose all his girlfriends.

c.) If done with 5 girlfriends?

Explanation / Answer

Let ABCD be the correct sequence.

Then there are 9 derrangements such that none of the letters go in the right envelope.

BADC, BCDA, BDAC,

CADB, CDAB, CDBA,

DABC, DCAB, DCBA.

b)Probability that he will lose all girlfriend=9/24=0.375

c)if done with 5 girlfriends: no of derrangements = 44

therefore ,Probability that he will lose all girlfriend=44/120=0.367

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