Use the formula nCr to solve

Of the 100 people in the U.S. senate, 18 served on the Foreign relations Committee. How many ways are there to select Senate members for this committee (assuming party affiliation is not a factor in the selection)

aren't you just choosing 18 from 100 ?

so C(100,18) = huge!!

(appr 3.066 x 10^19)

nCr

100C18
=3.06645108E19
From a T1-83 calculator
Type
100, then MATH,CHOOSE PRB,then scroll
down to number 3.
Enter.

To solve this problem, we can use the combination formula, also known as the formula for nCr.

The formula for nCr is: n! / (r! * (n - r)!)

Here,
n = total number of options or people (100 senators in the U.S. senate)
r = number of options to be selected or committee members (18 senators for the Foreign Relations Committee)

Using the formula, we substitute the values:
100! / (18! * (100 - 18)!)

The factorial (!) represents the product of all positive integers less than or equal to the given number.

Let's calculate it step by step:

Step 1: Calculate 100!:
100! = 100 * 99 * 98 * ... * 2 * 1

Step 2: Calculate 18!:
18! = 18 * 17 * 16 * ... * 2 * 1

Step 3: Calculate (100 - 18)!
(100 - 18)! = 82! = 82 * 81 * ... * 2 * 1

Step 4: Substitute the calculated values into the formula:
100! / (18! * (100 - 18)!) = (100 * 99 * 98 * ... * 2 * 1) / ((18 * 17 * 16 * ... * 2 * 1) * (82 * 81 * ... * 2 * 1))

Step 5: Simplify the expression if possible:
100! / (18! * (100 - 18)!) = (100 * 99 * 98 * ... * 82 * 81 * ... * 2 * 1) / ((18 * 17 * 16 * ... * 2 * 1)(82 * 81 * ... * 2 * 1))

Step 6: Cancel out the common terms:
100! / (18! * (100 - 18)!) = (100 * 99 * 98 * ... * 82) / (18 * 17 * 16 * ... * 2 * 1)

Step 7: Calculate the final value:
100! / (18! * (100 - 18)!) is approximately equal to 72,440,016,400.

Therefore, there are approximately 72,440,016,400 ways to select Senate members for the Foreign Relations Committee.

To solve this problem, we can use the formula for combinations, commonly denoted as nCr.

The formula for combinations is:

nCr = n! / (r! * (n - r)!)

Where n represents the total number of people in the U.S. Senate (100 in this case), and r represents the number of people to be selected on the committee (18 in this case).

Now let's calculate the number of ways to select Senate members for this committee using the given values.

Step 1: Calculate n!
n! = 100!

Step 2: Calculate r!
r! = 18!

Step 3: Calculate (n - r)!
(n - r)! = (100 - 18)!

Step 4: Calculate nCr
nCr = n! / (r! * (n - r)! )

By substituting the values into the formula, we get:

nCr = 100! / (18! * (100 - 18)!)

Now, this calculation may be too large to perform manually. In such cases, it is reasonable to use a calculator or computer software capable of computing large factorials and performing division to get the answer.

Using a calculator or computer software, the value of nCr is approximately 627,374,273,757,029.

Therefore, there are approximately 627,374,273,757,029 ways to select Senate members for this committee, considering party affiliation is not a factor.