First slide

Theorems of probability

Question

There are 5 letters and 5 addressed envelops. If the letters are put at random in the envelops, the probability that atleast one letter may be placed in wrongly addressed envelope is

Easy

A

$\frac{119}{120}$
B

$\frac{120}{343}$
C

$\frac{1}{1155}$
D

$\frac{139}{140}$

Solution

$n (S) = 5! = 120$
$P (a t l e a s t o n e) = 1 - P (n o n e)$

$= 1 - \frac{1}{120} \to a l l g o c o r r e c t p l a c e s$

$= \frac{119}{120}$

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