In how many ways can 3 letters be mailed in 6 mailboxes if each letter must be mailed in a different box? If the letters are not necessarily mailed in different boxes, how many ways are there of posting them? If the letters are mailed at random, and not necessarily in different boxes, what is the probability that all the letters are put in the same mailbox?

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Mathematics

31 December, 23:34

In how many ways can 3 letters be mailed in 6 mailboxes if each letter must be mailed in a different box? If the letters are not necessarily mailed in different boxes, how many ways are there of posting them? If the letters are mailed at random, and not necessarily in different boxes, what is the probability that all the letters are put in the same mailbox?

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Answers (1)

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Howard Knapp · Answer 1

Question 1: 120 ways

Question 2: 216 ways

Question 3: 1/36 = 0.278

Explanation:

Question 1: In how many ways can 3 letters be mailed in 6 mailboxes if each letter must be mailed in a different box?

The first letter may be mailed in any of the 6 mailboxes: 6

The second letter may be mailed in any of the other 5 mailboxes: 5

The third letter may be mailed in any of the other 4 mailboxes: 4

According to the fundamental counting principle, the total number of possible outcomes is the product of the possible outcomes for each event.

Thus, the number of ways 3 letters can be mailed in 6 mailboxes, if each letter must be mailed in a different box is 6 * 5 * 4 = 120.

Question 2: If the letters are not necessarily mailed in different boxes, how many ways are there of posting them?

Again, you must use the fundamental counting principle.

This time, since the letters are not necessarily mailed in different boxes, each one can be mailed in 6 boxes, and the total number of ways 3 letters can be mailed is:

6 * 6 * 6 = 216.

Question 3. If the letters are mailed at random, and not necessarily in different boxes, what is the probability that all the letters are put in the same mailbox?

The probability that all the letters are put in the same mailbox is:

number of favorable outcomes / number of total possible outcomes

number of favorable outcomes: 6

This is: the three letters are mailed in the first mailbox, or the three letters in the second mailbox, or the three letters in the third mailbox, or the three letters in the fourth mailbox, or the three letters in the fifth mailbox, or the three letters in the sixth mailbox: 6.

number of total possible outcomes: 216 calculated in the question number 2.

probability = 6 / 216 = 1/36 = 0.278