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?

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?

I believe b and c are related to the method used to finding a.)

Explanation / Answer

a) 4*3*2*1=24

b)24-1=23

probability=23/24

c)1)5*4*3*2*1=120 2)120-1=119 probability 119/120

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