Question

A total of 25 students have entered a spelling contest. There are 6 medals for first through sixth place that will be awarded. In how many different ways can the medals be awarded?

Answer 1

You would take 25 and the previous 5 numbers before and multiply them together

25*24*23*22*21*20=127,512,100

There are 127,512,000 ways

Answer 2

127512000 ways

Explanation:

Total number of students = 25

and number of medals to be distributed = 6 for first six place

Since order of medals [six place] matters

then permutation will be applied to calculate the different ways in which medals can be awarded.

Number of ways =
`^(n)P_(r)`

where n = 25 and r = 6

`^(n)P_(r)` =
`^(25)P_(6)` =
`((25!)/((25-6)!)`

`(25!)/(19!)`

= 25 × 24 × 23 × 22 × 21 × 20

= 127512000 ways