Page 98 - NUMINO Challenge_C2

Basic Concepts Picking a Leader

Electing a president and a vice president: The number of outcomes when
electing a president and a vice president from among students is

( 1).
Electing 2 representatives: The number of outcomes when electing 2
representatives from among the electing people is ( 1) 2.

Example Josh’s class is having an election. Find the number of outcomes when
electing 2 representatives from among 4 candidates in the following
ways.

President and vice president 2 representatives

Class Notes

The following tree diagrams show the number of ways a president and a vice

president can be elected from among 4 candidates: A, B, C, and D.

President Vice President Vice President Vice President Vice
A President B President C President D President

B A A A
C C B B
D D D C

If A, B, C, or D each is elected as president, there are ways to elect a vice

president. Therefore, the number of cases is 4 .

Even if the number of candidates is the same, the number of outcomes when
electing a president and a vice president is dif ferent from electing 2
representatives. In the table below, there are two outcomes when David and Julie
are each president and the other vice president but when both David and Julie are
1 of 2 representatives, there is just one outcome.

President Vice President Representatives

David Julie David, Julie
Julie David

Therefore, dividing the number of outcomes when electing a president and a vice
president by 2, gives the number of outcomes when electing 2 representatives.

42

Try It Again Find the number of cases when electing 2 representatives from
among 6 people.

95Number of Outcomes