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?
- 10 ways
- 15 ways
- 4 ways
- 20 ways **
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The correct answer is 10 ways.
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10
Yes, the correct answer is 10 ways.
To calculate the number of ways you can choose 2 pairs of jeans from 5, we can use the concept of combinations.
First, let's understand what a combination is. In mathematics, a combination is a selection of items from a larger set without regard to the order of the items. In this case, we want to select 2 pairs of jeans from a set of 5.
The number of ways to choose 2 pairs of jeans from 5 can be calculated using the formula for combinations, which is expressed as:
C(n, k) = n! / (k!(n-k)!)
Where:
- C(n, k) represents the number of combinations of n items taken k at a time.
- n! denotes n factorial, which means multiplying all positive integers from 1 to n.
Using this formula, we can calculate the number of ways to choose 2 pairs of jeans from 5.
C(5, 2) = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4 * 3 * 2 * 1) / (2 * 1 * 3 * 2 * 1)
= (5 * 4) / (2 * 1)
= 20 / 2
= 10
So, there are 10 ways to choose 2 pairs of jeans from 5.
Therefore, the correct answer is: 10 ways.