There are 6 different letters and 6 correspondingly addressed envelopes. If the letters are randomly put in the envelopes, what is the probability that exactly 5 letters go into the correctly addressed envelopes?

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Submitted by examrobotsa on

Q: 148 (IAS/2008)
There are 6 different letters and 6 correspondingly addressed envelopes. If the letters are randomly put in the envelopes, what is the probability that exactly 5 letters go into the correctly addressed envelopes?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,7,3,4,0,3

keywords: 

{'probability': [0, 3, 3, 0], 'envelopes': [0, 0, 1, 0], 'letters': [0, 0, 0, 3], 'different letters': [0, 0, 2, 0]}

Option 1, zero, is the correct answer. This situation refers to a derangement problem where no object appears in its proper place. If you randomly insert 6 distinct letters into 6 distinct envelopes, the chances of exactly 5 of them getting into their correctly addressed envelopes is zero. Here`s why:

If five letters are correctly sorted, it implies that the sixth letter also ends up in the correct envelope by default, defying the criteria of exactly 5 right placements. Therefore, the occurrence of having exactly five out of six correctly placed is impossible, leading to the probability as zero.

The other options - 1/6, 1/2, and 5/6 do not apply in this context. This disregards the fact that the sixth letter would automatically be in the correct envelope if the first five are correct, leading to all six letters being correctly sorted, not exactly 5.