Question

An art gallery has 11 vases.

How many ways can 6 of the vases be arranged in the display window?

Answer 1

To determine the number of ways 6 vases can be arranged in the display window, we can use the concept of permutations. In this case, there are 11 vases and we need to select 6 vases. Using the formula for permutations, we find that there are 55,440 ways to arrange the vases in the display window.

Step-by-step explanation:

To determine the number of ways 6 vases can be arranged in the display window, we can use the concept of permutations. Since order matters in this case, we can calculate the number of permutations using the formula:

P(n, r) = n! / (n-r)!

where P(n, r) represents the number of permutations of selecting r items from a set of n. In this case, n = 11 (total number of vases) and r = 6 (number of vases to be arranged). So, the number of ways the vases can be arranged is:

P(11, 6) = 11! / (11-6)!

Simplifying this expression:

11! / 5! = (11 × 10 × 9 × 8 × 7 × 6!) / 5!

Canceling out the common factors, we get:

11 × 10 × 9 × 8 × 7 = 55,440

Therefore, there are 55,440 ways to arrange 6 vases in the display window.

Answer 2

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 = (n!)/((n-r)!)`

here we have

n= 11

r= 6

substituting the values,

`11P_6 = (11!)/((11-6)!)`

`11P_6 = (11!)/((5)!)`

`11P_6 = (11 * 10 * 9 * 8*  7 * 6 * 5 * 4 * 3 * 2* 1)/((5 * 4 * 3 * 2* 1))`

`11P_6 = 11 * 10 * 9 * 8* 7 * 6`

`11P_6 = 332640`