How many combinations are possible? Assume the items are distinct. Show your work.:
7 items chosen 4 at a time
The formula for calculating 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 being chosen.
In this case, n = 7 and r = 4.
C(7, 4) = 7! / (4! * (7-4)!)
C(7, 4) = 7! / (4! * 3!)
C(7, 4) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (3 * 2 * 1))
C(7, 4) = 5040 / (24 * 6)
C(7, 4) = 5040 / 144
C(7, 4) = 35
Therefore, there are 35 possible combinations when choosing 4 items out of 7 distinct items.