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There are $4$ letter boxes in a post office. In how many ways can a man post $8$ distinct letters? $A)4 \times 8$  $B){8^4}$  $C){4^8}$  $D)P(8,4)$

Last updated date: 13th Jul 2024
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Hint: First we have to define what the terms we need to solve the problem are.
Since there are a total of eight distinct letters and we need to place or post into the four-letter boxes which are in the post office, also distinct means all letters are different from the other no one can be the same as.
In what way does the postman need to post those eight distinct letters?

We can try to solve this problem by separating the post office letter boxes; since there total four boxes in the post office, now let us the first box in that post office now we will try to place that eight distinct letters (no repetition of the post letters is allowed) and hence there are total eight ways (eight letters into the box one) hence $8$ ways .Similarly let in the second box in that post office now we will try to place that eight distinct letters (no repetition of the post letters is allowed) and hence there are total eight ways (eight letters into the box one).
Thus, repeating the same for the third and final boxes we get $8,8$ ways respectively;
So, we placed that letters in all the four boxes at $8,8,8,8$ ways
Hence to find total how many ways is the addition of the all terms or ways we get $8 + 8 + 8 + 8 = 32$
Thus option $A)4 \times 8$ is the only correct option.
Note: We are also able to solve this problem using the each of the given letters can go into each of the eight boxes and thus there are $4 \times 8 = 32$ number of the ways.
If the question is about repetition, the number of arrangements is the answer, which means the permutation of the option $D)P(8,4)$ is correct.