Question

An art gallery has 11 vases.
How many ways can 6 of the vases be arranged in the display window?

Answer 1

Answer:

6 of the vasescan be arranged in 332640 ways .

Step-by-step explanation:

Given:

Number of vases  = 11

To find:

Ways can 6 of the vases be arranged in the display window= ?

Solution:

Let us use permutation to find the number of  ways can 6 of the vases be arranged in the display window

So

11 position 6 = $11P_6$

$nP_r = \frac{n!}{(n-r)!}$

here we have

n= 11

r= 6

substituting the values,

$11P_6 = \frac{11!}{(11-6)!}$

$11P_6 = \frac{11!}{(5)!}$

$11P_6 = \frac{11 \times 10 \times 9 \times 8\times  7 \times 6 \times 5 \times 4 \times 3 \times 2\times 1}{(5 \times 4 \times 3 \times 2\times 1)}$

$11P_6 = 11 \times 10 \times 9 \times 8\times 7 \times 6$

$11P_6 = 332640$