Question

Dr. Orchid has 9 paintings she wants to hang side by side on her walls.
a) in how many ways can she arrange all 9 paintings?
b) if she wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display?

Answer 1

The number of ways Dr. Orchid can arrange all 9 paintings is 362880 and the number of ways she can choose the paintings she wishes to display is 126.

What is combination?

Combination is the way of arrangement or the collection of items in the particular order. The order of this group of items does not matter in the combination type of arrangement.

Dr. Orchid has 9 paintings she wants to hang side by side on her walls.

• a)Number of ways she can arrange all 9 paintings-

Total number of paintings is 9. She wants to arrange them side by side. Thus, the number of ways, she can arrange all 9 paintings is,

$9!=9\times8\times7\times6\times5\times4\times3\times2\times1\\9!=362880$

• b) Number of ways she can choose the paintings she wishes to display.

She wants to display 4 of the paintings. The number of arrangement of 4 painting from 9 paintings is,

$^9C_4=\dfrac{9!}{(9-4)!4!}\\^9C_4=\dfrac{9\times8\times7\times6\times5!}{5!\times4\times3\times2\times1}\\^9C_4=126$

Thus, the number of ways Dr. Orchid can arrange all 9 paintings is 362880 and the number of ways she can choose the paintings she wishes to display is 126.

Learn more about the combination here;

https://brainly.com/question/17139330

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