700 people are in a group. We\'ll use F to represent the first initial of their first name, L for the first initial of their last name. Each person is identified with a pair (F,L). At least how many people from this group have the same pairs (F,L) of initials of their first and last names? Solution There are 26 possibilites for F and 26 for L. So there are 676 different possibilities for unique (F,L) pairs. So atleast 24 of the pairs should match with some pair from the other 676. If all the 24 pairs are different, then we have 24 sets of people who have same pair of (F,L). So there are atleast 2 people who have the same pair of (F,L). This will be the minimum assuming 676 people span all the possibilities and other 24 people have unique pairs of (F,L)..

1. 700 people are in a group. We'll use F to represent the first initial of their first name, L for the
first initial of their last name. Each person is identified with a pair (F,L). At least how many
people from this group have the same pairs (F,L) of initials of their first and last names?
Solution
There are 26 possibilites for F and 26 for L. So there are 676 different possibilities for unique
(F,L) pairs. So atleast 24 of the pairs should match with some pair from the other 676. If all the
24 pairs are different, then we have 24 sets of people who have same pair of (F,L). So there are
atleast 2 people who have the same pair of (F,L). This will be the minimum assuming 676 people
span all the possibilities and other 24 people have unique pairs of (F,L).