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Question

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


A
75
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B
35
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C
57
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D
2520
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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 multiply
There 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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