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

The number of ways Dr. Orchid can arrange all 9 paintings and 4 paintings is, 362880 and 126 respectively.

What is arrangement?

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.

The number of possible ways to arrange is n!. Here, n is the number of objects.

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

• (A) Number of ways, she arranges all 9 paintings.

There are total 9 paintings. So the number of arrangement of these painting is,

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

• (B) Number of ways can she choose the paintings she wishes to display-

There are total 9 paintings, in which Dr. Orchid wants to display 4 of the paintings.  Thus, the number of ways can she choose the paintings she wishes to display is,

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

Hence, number of ways Dr. Orchid can arrange all 9 paintings and 4 paintings is, 362880 and 126 respectively.

Learn more about the arrangement here;

https://brainly.com/question/6032811

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