Question

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.)

---Select--- Yes No  . Let A be the set of 700 distinct people and let B be the  different unique combinations of first and last initials. If we construct a function from A to B, then by the  ---Select--- pigeonhole zero product mathematical induction  principle, the function must be  ---Select--- onto, one-to-one, not a one-to-one correspondence  . Therefore, in a group of 700 people, it is  ---Select--- possible, impossible,  that no two people have matching first and last

Answer 1

total possible unique combinations = no. of letters ^2 = 26*26 = 676

676<700 so by pigeonhole principle it is impossible that no two have same initials

ANSWER :

Yes Let A be the set of 700 distinct people and let B be the  different unique combinations of first and last initials. If we construct a function from A to B, then by the pigeonhole principle, the function must be one-to-one correspondence  . Therefore, in a group of 700 people, it is impossible, that no two people have matching first and last.

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