A parade organizer received 8 entries for floats. How many ways can he arrange 4 floats out of the 8 entries?
The organizer can arrange the floats in $8\times 7\times 6\times 5=\boxed{1680}$ ways.
To find the number of ways to arrange 4 floats out of 8 entries, we can calculate the combination.
The formula for calculating combinations is:
C(n, r) = n! / (r! * (n-r)!)
In this case, n = 8 (number of entries) and r = 4 (number of floats to be arranged).
Plugging in the values into the formula, we get:
C(8, 4) = 8! / (4! * (8-4)!)
C(8, 4) = 8! / (4! * 4!)
Now, let's calculate each factorial:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
4! = 4 x 3 x 2 x 1
Plugging these values into the formula:
C(8, 4) = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((4 x 3 x 2 x 1) * (4 x 3 x 2 x 1))
Now, let's calculate the numerator and denominator separately:
Numerator: 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Denominator: (4 x 3 x 2 x 1) * (4 x 3 x 2 x 1) = 24
Finally, we divide the numerator by the denominator:
C(8, 4) = 40,320 / 24
C(8, 4) = 1,680
Therefore, there are 1,680 ways to arrange 4 floats out of 8 entries.