Question

A committee is formed consisting of one representative from each of the 50 states in the United States, where the representative from a state is either the governor or one of the two senators from that state. How many ways are there to form this committee?

Answer 1

Answer:

717,897,987,691,852,588,770,249 ways

Step-by-step explanation:

Here we have to use the product rule.

It says if one event can occur in "m" ways and a second in "n" ways, then the two events can occur in "m × n" ways.

Given:

One representative from each of the 50 states in the United States.

There are 3 representative in each state (1 governor and two senators). It means 1 state can have 3 ways.

Using the product rule.

The number of ways to form the committee = 3 × 3 × 3 ...3(50 times)

= $3^{50}$

= 717,897,987,691,852,588,770,249 ways