Question

# What is the number of ways in which one can post $$5$$ letters in $$7$$ letter boxes?

A
75
B
35
C
57
D
2520

Solution

## The correct option is A $$7^5$$Each of the $$7$$ choices that could be made for the first letter there are $$7$$ choices that can be made for the second letter, and the choices multiplyThere are $$7\times7$$ possibilities for where the first $$2$$ letters will be placed, and for each of those cases, There are $$7$$ possibilities for what to do with the third letter. For each letter there are exactly $$7$$ choices, and the number of possible outcomes is the product of all those $$7's.$$The calculation done as $$7\times7\times7\times7\times7=7^5$$ is based on the fact that for each letter you have exactly $$7$$ choices$$\therefore$$ Option A is correct Mathematics

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