Question

There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. How many ways can we choose a Senator from a chosen state?

Answer 1

We can not choose a senator again from the state from where we have already chosen a senator.

There are 2 number of ways we can chose a senator from the one chosen state.

Total number of ways of making the 3 senator committee = 940800

Explanation:

Given that There are 2 Senators from each of 50 states.

To find:

The number of ways to make a 3 senator committee so that no two members are from the same state = ?

Solution:

There are a total of 2
`*` 50 = 100 senators

First of all, we can select any one from these 100.

So, number of ways of choosing the first senator = 100 (50 states left and there are 2 senators so 50
`*` 2 = 96)

Now, we need to choose the 2nd senator.

As per the given statement, we can not choose the senator from the state from which we have already chosen a senator. The one state will not be considered now.

So, number of ways of choosing the 2nd senator = 98 (49 states left and there are 2 senators so 49
`*` 2 = 98)

Now, we need to choose the 3rd senator.

As per the given statement, we can not choose the senator from the state from which we have already chosen a senator. Two states will not be considered now.

So, number of ways of choosing the 3rd senator = 96 (48 states left and there are 2 senators so 48
`*` 2 = 96)

Total number of ways of making the 3 senator committee = 100
`*` 98
`*` 96 = 940800