Question

1. Dr. Orchid has 9 paintings she wants to hang side by side on her wall.
(a) In how many ways can she arrange all 9 paintings? Show your work.
(b) If she only wants to display 4 of the paintings, in how many ways can she choose the paintings she
wishes to display? Show your work.
Answer:

Answer 1

The number of ways to arrange the 9 paintings is 362880, and there are 126 ways to display only 4 out of the 9 paintings

Part A: The number of arrangements.

The number of paintings is given as:

n = 9

The number of arrangement is then calculated using:

n! = 9!

Evaluate the factorial

n! = 362880

Part B: The number of selection

To select 4 paintings from a total of 9, we make use of the following combination formula

Ways  = 9C4

Evaluate the above expression using a calculator

Ways  = 126

Hence, there are 126 ways to display only 4 out of the 9 paintings

Read more about combination at:

https://brainly.com/question/11732255

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