There are four letters and four addressed envelopes. The probability that all letters are not dispatched in the right envelope is:

\frac{20}{24}

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\frac{21}{24}

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\frac{23}{24}

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Solution

The correct option is C $\frac{23}{24}$
Given that there are $4$ letters and $4$ envelopes.
The probability that all letters are not dispatched in the right envelope is equal to one minus probability that all letters are dispatched to right envelopes.
The number of ways all the letters are dispatched to right envelopes is $1$ .
The required probability is $\frac{4! - 1}{4!} = \frac{23}{24}$ .
Therefore the correct option is $C$ .

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