How many ways can an IRS auditor select 5 of 9 tax returns
9C5 if order does not matter
9P5 if it does
To find the number of ways an IRS auditor can select 5 tax returns out of a pool of 9, we can use the concept of combinations. The formula for combinations is given by:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of items and k is the number of items to be selected.
In this case, n = 9 (total number of tax returns) and k = 5 (number of tax returns to be selected). Now we can calculate the number of ways:
C(9, 5) = 9! / (5!(9-5)!)
Simplifying further,
C(9, 5) = (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1)
The factorials in the numerator and denominator cancel out, leaving us with:
C(9, 5) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
C(9, 5) = 126
Therefore, there are 126 different ways the IRS auditor can select 5 of the 9 tax returns.