how many ways can an IRS auditor select 5 of 12 tax returns for an audit?
462
792
To determine the number of ways the IRS auditor can select 5 tax returns out of 12 for an audit, we can use combinatorics, specifically the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n - r)!)
Where:
C(n, r) represents the number of combinations of n items taken r at a time,
n! represents the factorial of n (n factorial), and
r! and (n - r)! represent the factorials of r and (n - r), respectively.
In this case, we want to find C(12, 5).
By substituting the values into the formula, we get:
C(12, 5) = 12! / (5!(12 - 5)!)
Calculating this:
12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 479,001,600
5! = 5 × 4 × 3 × 2 × 1 = 120
(12 - 5)! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
Substituting these values back into the formula:
C(12, 5) = 479,001,600 / (120 × 5,040)
After simplification, we find:
C(12, 5) = 792
Therefore, there are 792 ways the IRS auditor can select 5 tax returns out of 12 for an audit.