Question

Find the number of ways in which one can post 5 letters in 7 boxes.

Answer 1

Now we want to arrange 5 letters in 7 boxes. To do so we will first select 5 boxes out of 7. Now once we have 5 boxes we will arrange 5 letters in 5 boxes. We know this can be done in all possible ways.

Complete step-by-step solution:

Now we want to find the number of ways in which one can post 5 letters in 7 boxes.

Now first let us select 5 boxes out of 7 boxes.

To select 1 box for the first letter there are 7 choices available.

Similarly, to select 1 box for the second letter there are again 7 choices available as no restriction is there. So, both are independent events.

Similarly, to select 1 box for the third letter there are again 7 choices available and so on.

Hence the number of ways to select 5 boxes out of 7 boxes is given by $7\times 7\times 7\times 7\times 7=7^{5}$

Hence the total number of ways =$7^{5}$.

Note: Now note that we first select the boxes and then arrange the letter. Since the two events take place one after another we multiply the number of possibilities and not add them. Consider that both the events are independent events.