You have a frame that holds three pictures. You pulled out your favorite five photos. How many sets of three are there?
Make a list of all the possible combinations using the numbers 1 through 5 to represent the photos.
To find the number of sets of three photos, we can use the concept of combinations.
The number of combinations of n objects taken r at a time is given by the formula:
nCr = n! / (r!(n-r)!)
In this case, we have 5 photos (n = 5) and we want to choose sets of three (r = 3).
Let's calculate the number of sets of three photos:
5C3 = 5! / (3!(5-3)!)
= 5! / (3!2!)
= (5 * 4 * 3!) / (3! * 2 * 1)
= (5 * 4) / (2 * 1)
= 10 / 2
= 5
Therefore, there are 5 sets of three photos.
Now let's list all the possible combinations using the numbers 1 through 5 to represent the photos:
1. 1, 2, 3
2. 1, 2, 4
3. 1, 2, 5
4. 1, 3, 4
5. 1, 3, 5
6. 1, 4, 5
7. 2, 3, 4
8. 2, 3, 5
9. 2, 4, 5
10. 3, 4, 5