Question 1210159
Let's break this problem down step by step.

**1. Total Number of Senators**

* There are 50 states, and each state has 2 senators, so there are $50 \times 2 = 100$ senators.

**2. Choosing the States**

* We need to form a committee of 5 senators, and no two senators can be from the same state.
* First, we need to choose 5 states out of the 50 states. The number of ways to do this is $\binom{50}{5}$.

**3. Choosing the Senators from Each State**

* For each of the 5 chosen states, we have 2 senators to choose from.
* Since we need to choose one senator from each of the 5 states, we have 2 choices for each state.
* Therefore, we have $2^5$ ways to choose the senators from the selected states.

**4. Calculating the Total Number of Ways**

* To get the total number of ways to form the committee, we multiply the number of ways to choose the states by the number of ways to choose the senators from those states.

Total ways = $\binom{50}{5} \times 2^5$

**5. Performing the Calculations**

* $\binom{50}{5} = \frac{50!}{5!45!} = \frac{50 \times 49 \times 48 \times 47 \times 46}{5 \times 4 \times 3 \times 2 \times 1} = 2,118,760$
* $2^5 = 32$

Total ways = $2,118,760 \times 32 = 67,800,320$

**Therefore, there are 67,800,320 ways to form a committee with 5 senators, in which no two of the senators are from the same state.**