Question

In how many ways can 3 letters be posted into 6 post-boxes (If the post-box can hold a maximum of one letter)?

• A. 10
• B. 20
• C. 60
• D. 120

Answer 1

The correct option is D 120

The letter boxes can be selected in 6C3 ways $=\frac{(6\times 5\times 4)}{(1\times 2\times 3)}=20$
The letters can be arranged among these boxes in 3! ways = 6
Hence, The total no. of possibilities $=20\times 6=120$

Special Case : If there were no restrictions (ie. If any no. of letters can be posted in each box)
The first letter can be posted in 6 boxes.
Second and third letters can also posted in 6 ways each.
Hence, the total no. of possibilities = 6$\times$6$\times$6
= 216