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In a group of 700 people, must there be 2 who have matching first and last initials? Why? (Assume each person has a first and last name.) Correct: Your answer is correct. . Let A be the set of 700 distinct people and let B be the 52 Incorrect: Your answer is incorrect. different unique combinations of first and last initials. If we construct a function from A to B, then by the Correct: Your answer is correct. principle, the function must be Correct: Your answer is correct. . Therefore, in a group of 700 people, it is Correct: Your answer is correct. that no two people have matching first and last initials.

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Answer:

Yes, there are only 676 different possibilities, which is less than the number of people in the group.

Step-by-step explanation:

Assuming that the English alphabet has 26 different letters, the number of possible combinations of first and last name initials is:

[tex]n = 26*26\\n=676[/tex]

If we try to assign a different combination to each person in the group, it would only be possible to do it for the first 676 people, while the remaining 24 would have a repeated first and last initial. Therefore, the answer is yes, there must be 2 people who have matching first and last initials.

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