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

Answer:

127512000 ways

Step-by-step 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

$^{n}P_{r}$ = $^{25}P_{6}$ = $\frac{(25!}{(25-6)!}$

$\frac{25!}{19!}$

= 25 × 24 × 23 × 22 × 21 × 20

= 127512000 ways