Please answer all parts Reba has 11 paintings she wants to hang side by side on her wall.
A. If she only wants to display 8 of the paintings, in how many ways can she choose 8 paintings she wishes to
eventually display? Show your work.
B. In how many ways can she arrange all 11 paintings? Show your work.
C. If Reba wants to have the 10 out of 11 paintings in specific places, how many ways could she order the 10
paintings? Show your work.

A) 165

B) 39, 916, 800

C) 39, 916, 800

Step-by-step explanation:

Reba has 11 paintings in total.

Part A)

She only wants to display 8 out of the 11 total.

In this case, the order does not matter.

In other words, we can use a combination. Since she only wants 8 out of 11, the number of possible ways will be 11C8.

This is equivalent to:

Hence, the number of possible combinations is 165.

Part B)

She wants to know in how many ways she can arrange all 11 paintings.

Thus, it will simply be the factorial of the amount of items.

We have 11 items. So, the number of ways she can arrange them is 11!.

Using a calculator, we can see that:

Hence, Reba has a total of 39, 916, 800 ways to arrange all 11 paintings.

Part C)

In this case, Reba wants to arrange 10 out of 11 paintings in specific places.

So, order does matter. Thus, we will use a permutation.

She wants to arrange 10 out of the 11. So, the number of combinations possible will be 11P10.

So:

Or, as previously determined, there will be 39, 916, 800 distinct ways.

$5.41

step-by-step explanation:

$20 - $14.51 = $5.49.