Question

There are $6$ letters and $3$ post-boxes. The number of ways in which these letters can be posted is

• A. $6^3$
• B. $3^6$
• C. ${}^6{C}_3$
• D. ${}^6{P}_3$

Answer 1

Answer: (B)

$3^6$

There are 6 letters and 3 post boxes

Lets consider letter $1,2,3,4,5,6$ as $L1,L2,L3,L4,L5,L6$respectively.

Also post boxes $1,2,3$ as $P1,P2,P3$ respectively

Now L1 could be placed in any of $P1,P2,P3.$ Thus, there are $3$ ways to post $L1$

Hence, there are $3\times 3\times 3\times 3\times 3\times 3$ =$3^6$ ways to post $6$ letters in $3$ post boxes.