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)
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C(n,r) is the same as nCr
and is defined as
n!/(r!(n-r)!)
To solve this problem, we can use the formula for combinations, also known as binomial coefficients or nCr.
The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of items to choose from and r is the number of items to choose.
In this case, n = 100 (total number of people in the U.S. Senate) and r = 18 (number of people needed for the Foreign Relations Committee).
Using the formula, we can calculate the number of ways to select Senate members for the committee:
nCr = 100! / (18!(100-18)!)
= 100! / (18! * 82!)
Here, the exclamation mark (!) represents the factorial of a number, which is the product of all positive integers less than or equal to that number.
Calculating factorials for large numbers can be computationally intensive. However, many calculators and computer programs have built-in functions for calculating factorials and combinations.
So, using a calculator or computer program, you can evaluate the expression 100! / (18! * 82!) to find the answer to be:
nCr = 100! / (18! * 82!) = 35,868,900 ways
Therefore, there are 35,868,900 ways to select Senate members for the Foreign Relations Committee, assuming party affiliation is not a factor in the selection.