I have 7 different pairs of jeans and want to take 2 with me on vacation. how many different ways can you pick 2 pairs of jeans to take on vacation.

sorry for not proofing before

I know there's a way of figuring this out mathematically -- but I don't know it.

However, if you labeled each pair with a letter from A to G, you could figure it this way.

AB, AC, AD, AE, AF, AG
BC, BD, BE, BF, BG
CD, CE, CF, CG
DE, DF, DG
EF, EG
FG

That looks like 21 ways.

No worries! Let's solve this problem step by step.

To figure out the number of different ways you can choose 2 pairs of jeans from 7 different pairs, we can use the combination formula.

The combination formula is given by:

C(n, r) = n! / (r! * (n - r)!)

Where:
- n is the total number of items (in this case, the number of pairs of jeans you have, which is 7)
- r is the number of items you want to choose (in this case, 2)
- "!" denotes the factorial function, which means multiplying a number by all positive whole numbers less than itself

Plugging in the values, we get:

C(7, 2) = 7! / (2! * (7 - 2)!)

Calculating the factorials:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
2! = 2 * 1 = 2
(7 - 2)! = 5! = 5 * 4 * 3 * 2 * 1 = 120

Substituting these into the formula:

C(7, 2) = 5040 / (2 * 120)

Simplifying the expression:

C(7, 2) = 5040 / 240

Dividing:

C(7, 2) = 21

Therefore, there are 21 different ways you can choose 2 pairs of jeans to take on vacation from the 7 different pairs you have.