How many outfit combinations are possible with 1 pair of sneakers, 3 tee-shirts and 2 pairs of jeans? Drawing a diagram might help to illustrate your strategy.
1 pair of sneakers for each outfit. #3 tee shirts with 1 pair of jeans and #3 with the 2nd pair of jeans. That is 6 outfits in all.
Sra
30
To determine the number of outfit combinations, we need to multiply the number of choices for each item together.
In this case, we have:
- 1 pair of sneakers
- 3 tee-shirts
- 2 pairs of jeans
To visually represent the possible combinations, we can use a diagram.
First, draw a vertical line for each category (sneakers, tee-shirts, jeans).
Then, divide each category line into segments, with one segment for each item.
Sneakers:
------
-
Tee-shirts:
-------
-------
-------
Jeans:
------
-
-
Now, we'll fill in the combinations by selecting one option from each category and extending lines connecting them.
Sneakers:
-----
- |
Tee-shirts:
------
|
-----|-----
- |
Jeans:
-----
|
------|------
By following the lines, we can count all the possible combinations of items. Each line connecting an item from one category to the next represents a unique combination.
In this case, there are 1 option for sneakers, 3 options for tee-shirts, and 2 options for jeans.
To find the total number of combinations, multiply the number of options in each category together:
1 (sneakers) x 3 (tee-shirts) x 2 (jeans) = 6
Therefore, there are 6 possible outfit combinations with 1 pair of sneakers, 3 tee-shirts, and 2 pairs of jeans.
One suitable diagram here is a probability or combinations tree. Hard to show as we can't draw picures but I'll do my best.
On the LHS start with the sneakers and then add each teashirt (I have labelled them 1 to 3.
teashirt1
sneakers teashirt2
teashirt3
It is possible to wear a pair of jeans with each teashirt so we can now show.
jeans1
teashirt1 jeans2
sneakers teashirt2 jeans1
jeans2
teashirt3 jeans1
jeans2
Normally we would join up the items with lines to make a 'tree'
At the far right we put the combinations by reading along the branches of the tree.
sneakers, teashirt1, jeans1
sneakers, teashirt1, jeans2
sneakers, teashirt2, jeans1
sneakers, teashirt2, jeans2
sneakers, teashirt3, jeans1
sneakers, teashirt3, jeans2
so 6 possible.