In how many ways can 3 letters be posted in 4 | vedclass

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(B) Each of the $3$ letters can be posted in any of the $4$ letter-boxes.Since each letter has $4$ choices,the total number of ways to post $3$ letter

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(B) Each of the $3$ letters can be posted in any of the $4$ letter-boxes.Since each letter has $4$ choices,the total number of ways to post $3$ letters in $4$ letter-boxes is $4 	imes 4 	imes 4 = 4^3 = 64$.However,the condition states that all letters should not be posted in the same letter-box.There are $4$ cases where all $3$ letters are posted in the same box (i.e.,all in box $1$,all in box $2$,all in box $3$,or all in box $4$).Therefore,the required number of ways is $64 - 4 = 60$.

In how many ways can $3$ letters be posted in $4$ letter-boxes,if all the letters are not posted in the same letter-box?

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