How many ways can an IRS auditor select 4 of 9 tax returns for an audit?
number of ways
= C(9,4)
= 9!/(5!4!)
= 126
To find the number of ways an IRS auditor can select 4 tax returns for an audit out of a pool of 9 tax returns, we can use the concept of combinations. In mathematics, combinations represent the number of ways to choose a specific number of items from a larger set without regard to the order in which they are chosen.
The formula to calculate combinations is:
C(n, r) = n! / (r! * (n - r)!)
Where:
- n is the total number of items in the set (in this case, 9 tax returns)
- r is the number of items to be chosen (in this case, 4 tax returns)
- n! represents the factorial of n, which signifies multiplying all positive integers up to n
Let's plug in the values and calculate the number of ways the IRS auditor can select 4 tax returns for an audit:
C(9, 4) = 9! / (4! * (9 - 4)!)
Now, let's break down the calculation step by step:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
4! = 4 x 3 x 2 x 1
(9 - 4)! = 5! = 5 x 4 x 3 x 2 x 1
Plugging the values into the combination formula:
C(9, 4) = (9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((4 x 3 x 2 x 1) x (5 x 4 x 3 x 2 x 1))
After simplifying:
C(9, 4) = 126
Therefore, there are 126 different ways for the IRS auditor to select 4 tax returns out of a pool of 9 tax returns for an audit.
To determine the number of ways an IRS auditor can select 4 tax returns out of 9 for an audit, we can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items being selected.
Plugging in the values for our problem:
n = 9 (total number of tax returns)
r = 4 (number of tax returns being selected)
C(9, 4) = 9! / (4!(9-4)!)
= 9! / (4!5!)
= (9 * 8 * 7 * 6 * 5!) / (4 * 3 * 2 * 1 * 5!)
= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
= 9 * 2 * 7
= 126
Therefore, there are 126 ways the IRS auditor can select 4 tax returns out of 9 for an audit.