If three letters can be posted to any one of | vedclass

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(A) The total number of ways to post $3$ letters to $5$ different addresses is $5^3 = 125$.To post the letters to exactly $2$ addresses,we first selec

Vedclass · Accepted Answer

$\frac{12}{25}$

Vedclass · Answer

(A) The total number of ways to post $3$ letters to $5$ different addresses is $5^3 = 125$.To post the letters to exactly $2$ addresses,we first select $2$ addresses out of $5$,which can be done in $^5C_2 = 10$ ways.For each selection of $2$ addresses,each of the $3$ letters can be posted to either of the $2$ addresses,giving $2^3 = 8$ ways. However,this includes the cases where all $3$ letters are posted to only $1$ address (either the first or the second),so we subtract these $2$ cases.Thus,the number of favorable ways is $^5C_2 	imes (2^3 - 2) = 10 	imes 6 = 60$.The required probability is $\frac{60}{125} = \frac{12}{25}$.

If three letters can be posted to any one of the $5$ different addresses,then the probability that the three letters are posted to exactly two addresses is:

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