a person writes 4 letters to 4 of his girl friends and addresses 4 envelopes (on

Question

a person writes 4 letters to 4 of his girl friends and addresses 4 envelopes (one to each) he places those letters in the envelopes at random. Let a = event that all letters go correctly.
1.Find p(a) 2. Let a = event that no letter goes to the right envelope. Find p(a) a person writes 4 letters to 4 of his girl friends and addresses 4 envelopes (one to each) he places those letters in the envelopes at random. Let a = event that all letters go correctly.
1.Find p(a) 2. Let a = event that no letter goes to the right envelope. Find p(a) a person writes 4 letters to 4 of his girl friends and addresses 4 envelopes (one to each) he places those letters in the envelopes at random. Let a = event that all letters go correctly.
1.Find p(a) 2. Let a = event that no letter goes to the right envelope. Find p(a)

Explanation / Answer

1.

There is only 1 way to send the letters.

However, there are a total of 4! = 24 ways to send them

Then, P(a) = 1/24 = 0.0416667 [ANSWER]

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2.

For the first letter, there are 3 ways to get it wrong.

For the second letter, there are 2 ways to get it wrong.

For the third letter, there is 1 way to get it wrong.

The fourth letter will automatically be wrong, then.

Thus, there are 3*2*1 = 6 ways to get them all wrong.

Thus,

P(a) = 6/24 = 1/4 = 0.25 [ANSWER]

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