Andrea Betty Joyce Karen and Paula are starters on their school basketball team . How many different groups of three can be chosen for a photo?
If order (in the photo) is not important, then we choose 3 from 5, which is 5C3=5!/(3!2!)=10
To find the number of different groups of three that can be chosen for a photo, we can use combinations. A combination is a selection of items without regard to the order in which they are arranged.
In this case, we want to choose 3 players out of a group of 5 (Andrea, Betty, Joyce, Karen, and Paula). The formula for combinations is given by:
C(n, r) = n! / ((r!)(n - r)!)
Where n is the total number of items and r is the number of items chosen.
In our case, n = 5 (the total number of players) and r = 3 (the number of players we want to choose).
Plugging the values into the formula, we have:
C(5, 3) = 5! / ((3!)(5 - 3)!)
C(5, 3) = (5 × 4 × 3!) / ((3 × 2 × 1)(2 × 1))
C(5, 3) = (5 × 4) / (2 × 1)
C(5, 3) = 10
Therefore, there are 10 different groups of three that can be chosen for a photo.