You own 9 pairs of pants and want to take 4 of them with you on vacation. In how many ways can you choose 4 pairs of pants to bring?
The order in which the pants are chosen doesn't matter, so this is a combination problem. We want to choose 4 pants out of 9, which we can write as:
9 C 4
Using the formula for combinations, we get:
9 C 4 = 9! / (4! * 5!) = (9*8*7*6) / (4*3*2*1) = 126
Therefore, there are 126 ways to choose 4 pairs of pants out of 9.
To determine the number of ways you can choose 4 pairs of pants from 9 pairs, we can use the concept of combinations, specifically, the formula for determining combinations.
The formula for combinations is given by:
nCr = n! / (r!(n-r)!)
where n represents the total number of items, r represents the number of items to be chosen, and ! denotes the factorial operation.
In this case, you have 9 pairs of pants and want to choose 4 of them. Since each pair of pants is considered as one item, you have a total of n = 9 items and want to choose r = 4 items.
Plugging in these numbers into the combination formula, we get:
9C4 = 9! / (4!(9-4)!)
Simplifying further:
9C4 = 9! / (4!5!)
Calculating the factorials:
9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
4! = 4 × 3 × 2 × 1
5! = 5 × 4 × 3 × 2 × 1
Substituting the factorials into the equation:
9C4 = (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((4 × 3 × 2 × 1)(5 × 4 × 3 × 2 × 1))
Cancelling out common factors:
9C4 = (9 × 8 × 7 × 6) / (4 × 3 × 2 × 1)
Performing the multiplication and division:
9C4 = 3024 / 24
Simplifying further, we get:
9C4 = 126
Therefore, there are 126 different ways you can choose 4 pairs of pants to bring on vacation.