Kendra bought 4 paintings and wants to hang them side by side on a wall in her bedroom. However, only 3 of the paintings will fit side by side on this wall. How many different ways can Kendra arrange 3 of the 4 paintings on the wall?
All you want is the number of permutations for 3 out of 4:
4P3 = 4*3*2 = 24
You can pick the first in 4 ways.
Now there are 3 choices for the 2nd,
and 2 left for the 3rd.
To solve this problem, we can use combinatorics. The number of ways Kendra can arrange 3 out of the 4 paintings on the wall is given by the concept of combinations.
The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items (paintings) and r is the number of items (paintings) to be chosen.
In this case, n = 4 (the total number of paintings) and r = 3 (the number of paintings to be chosen).
Plugging these values into the formula:
C(4, 3) = 4! / (3!(4-3)!)
= 4! / (3! * 1!)
= (4 * 3 * 2 * 1) / (3 * 2 * 1 * 1)
= 4
Hence, there are 4 different ways Kendra can arrange 3 out of the 4 paintings on the wall.