The population of a town is 20,000. If each resident has

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QUESTION:

The population of a town is 20,000. If each resident has three initials, is it true that at least two people have the same initials?

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QUESTION:

The population of a town is 20,000. If each resident has three initials, is it true that at least two people have the same initials?

ANSWER:

Step 1 of 2

Let  be sets with  elements respectively, then there are  ways in which we choose an element of  first then and finally an element.

Here, let be the set of all possible outcomes of the ith initial.

Then,

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