Question

There are 30 students in a class. Choose the statement that best explains why at least two students have last names that begin with the same letter. Multiple Choice

Using the pigeonhole principle, in any class of 30 students there must be at least two students who have last names that begin with the same letter since there are more than 2 students in the class.
Using the pigeonhole principle, in any class of 30 students there must be exactly two students who have last names that begin with the same letter since there are only 26 letters in the alphabet.
Using the pigeonhole principle, in any class of 30 students there must be at least two students who have last names that begin with the same letter since there are only 26 letters in the alphabet.
Using the pigeonhole principle, in any class of 30 students there must be at least two students who have last names that begin with the same letter since there are more than 2 letters in the alphabet.

Answer 1

Answer:

Using the pigeonhole principle, in any class of 30 students there must be at least two students who have last names that begin with the same letter since there are only 26 letters in the alphabet.

Explanation:

The pigeonhole principle states that if k+1 objects are placed in l holes, there must be at-least one hole where more than one objects are placed. So is the case with the first letter of last names of 30 students as there are only 26 unique alphabets in English language.

Answer 2

The statement that best explains why at least two students have last names that begin with the same letter is: (c) Using the pigeonhole principle, in any class of 30 students there must be at least two students who have last names that begin with the same letter since there are only 26 letters in the alphabet.

Names in the English language begin with upper case letters A to Z.

There are 26 upper case letters in the English language.

The number of students in the class is said to be 30.

Using  the pigeonhole principle, if there are n items then there must be at least m containers such that:

m > n

Assume that the first 26 students have their first names to be from A to Z, then at least one of the remaining 4 students would have his name to begin with any of letter A to Z.

Hence, the true statement is (c)

Read more about pigeonhole principle at:

https://brainly.com/question/23131670