Envelope and Letter

Logic Level 2

I have 5 envelopes and 5 letters (outside the envelope) on the table. Each letter goes to a distinct envelope.

Suddenly the light goes off and I put all the letters in the envelopes randomly (not knowing which is which).

What is the probability that exactly 4 letters are in right envelopes?

Note: I did not put more than 1 letter in any envelope.

none of the above 1/16 1 1/32 0 4/5 1/5

Saad Khondoker by Saad Khondoker , 21, Bangladesh

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1 solution

Saad Khondoker
Jan 20, 2021

The answer is 0 because if 4 envelopes have correct letters, that leaves 1 letter which goes to the remaining envelope.

So if 4 are correctly placed the 5th one is going to be correct automatically.

2 Helpful 3 Interesting 0 Brilliant 2 Confused

May I suggest that if you put it in the envelope, you yourself have no way of knowing whether or not the system is true. Randomly speaking, you can get 4 letters in the right envelope around 1/120 of the time, same with getting the correct combination. This is because the way factorials are involved in permutations.

Christian Colangelo - 3 months, 3 weeks ago

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the question says exactly 4 right that means 4 right 1 wrong which is impossible.

Saad Khondoker - 3 months, 3 weeks ago

Oh I see, good job on this one.

Christian Colangelo - 3 months, 2 weeks ago

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