In how many ways can 7 letters be posted in 4 letter boxes? - Vidyadip

Question

In how many ways can $7$ letters be posted in $4$ letter boxes?

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Answer

Total number of ball $= n = 5$
Number of boxes $= r = 3$
$5$ different balls can be distributed among three boxes in $^5P_3$ ways.
$^5\text{p}_3= \frac{5!}{(5-3)!}= \frac{5!}{2!}=\frac{5\times 4\times 3\times 2\times 1}{2 \times 1}=60.$
In 60 ways 5 different balls can be distributed among three boxes.

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