Question

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 1

She can arrange the 9 paintings in 362,880 different ways, and she can select 126 different combinations of 4.

In how many ways can she display the 9 paintings?

• For the first position, she has 9 options.
• For the second position, she has 8 options (one is already taken).

And so on for the rest of the positions.

The total number of different combinations is equal to the product between the numbers of options:

C = 9*8*7*6*5*4*3*2*1 = 9! = 362,880

b) This will be given by the combinations of 4 out of 9, or:

C(9, 4), where:

$C(9, 4) = \frac{9!}{(9 - 4)!*4!} = \frac{9*8*7*6}{4*3*2*1} = 126$

She can select 126 different combinations of 4 paintings.

If you want to learn about combinations:

https://brainly.com/question/11732255

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