Question

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

• A. $63$
• B. $60$
• C. $77$
• D. $81$

Answer 1

The correct option is B $60$

No. of ways $=$ Total ways of posting $3$ letters $-$ No. of ways in which all letters are posted in the same letter-box

Now, as there are $4$ letter-boxes therefore,

No. of ways in which all letters are posted in same letter-box $=4$( Either all letters are posted in box 1 or in box 2 or in box 3 or in box 4)

Each letter can be posted in 4 letter-boxes

$\therefore$ Total ways of posting $3$ letters is $4\times 4\times 4=64$

No. of ways $=64-4=60$

Hence, $\left(B\right)$