There are two ways to approach this problem: using the permutation formula or using combinatory reasoning.
Permutation formula:
The number of permutations of n distinct objects taken k at a time is given by:
nP(k) = n! / (n - k)!
where n! (read as "n factorial") is the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
In this case, we want to take 2 pairs of jeans out of 5. Therefore, n = 5 and k = 2. Plugging these values into the formula, we get:
nP(k) = 5P2 = 5! / (5 - 2)! = 5 x 4 x 3 / 3 x 2 x 1 = 10
Therefore, there are 10 ways to choose 2 pairs of jeans out of 5.
Combinatory reasoning:
Another way to solve this problem is to use combinatory reasoning. We can think of it as follows: we have 5 jeans, and we want to choose 2 of them. This means that we need to form pairs of jeans. The first pair can be chosen from any of the 5 jeans, and the second pair can be chosen from the remaining 4 jeans (since we cannot choose the same pair twice). Therefore, the total number of ways to choose 2 pairs of jeans out of 5 is:
5 x 4 / 2 x 1 = 10
where we divide by 2 x 1 to account for the fact that the order of the pairs does not matter.
Therefore, both methods give the same result: there are 10 ways to choose 2 pairs of jeans out of 5.
You own 5 pairs of jeans and want to take 2 of them with you on vacation. In how many ways can you choose 2 pairs of jeans?
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