Question

after a bride has interviewed 7 djs to play at her wedding, her fiance tells her she needs to narrow it down to 2 djs. in how many ways can she rank the 2 djs?

Answer 1

There are 42 ways for the bride to rank the 2 DJs out of the initial selection of 7.

What are the ways that the selection can be done

If the bride needs to narrow down the selection from 7 DJs to 2 and rank those 2 DJs, the number of ways she can do this is calculated using the permutation formula for selecting and arranging k of n

The formula for permutations is given by:

`\[ P(n, k) = (n!)/((n - k)!) \]`

Where:

n = Total number of items (in this case, the number of DJs = 7)

k = Number of items to be selected and ranked (in this case, she needs to rank 2 DJs)

Let's calculate the number of ways she can rank the 2 DJs:

`P(7, 2) = (7!)/((7 - 2)!) \]`

`\[ P(7, 2) = (7!)/(5!) \]`

`\[ P(7, 2) = (7 * 6 * 5!)/(5!) \]`

`\[ P(7, 2) = 7 * 6 = 42 \]`

Therefore, there are 42 ways for the bride to rank the 2 DJs out of the initial selection of 7.