A person write 4 letters and addresses 4 envelopes. If the letter… - Vidyadip

MCQ

A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is

A
$\frac{1}{4}$
B
$\frac{11}{24}$
C
$\frac{15}{24}$
✓
$\frac{23}{24}$

✓

Answer

Correct option: D.

$\frac{23}{24}$

Total number of ways of placing four letters in 4 envelops = 4 = 24
All the letters can be dispatched in the right envelops in only one way. Therefore, the probability that all the letters are placed in the right envelops is $\frac{1}{24}$.
Hence, probability that all the letters are not placed in the right envelops $=1-\frac{1}{24}=\frac{23}{24}$

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