A teacher wants to award prizes for 1st, 2nd, 3rd, 4th and 5th in the class of

30. In how many ways can the prizes be awarded (assume no two students

tie) ?

2,052,086,400.

Step-by-step explanation:

Permutation

Pr = n! / (n-r) !

30P5 = 30! / (30-5)

30P5 = 30x29x28x27x26x25! / 25!

(Just cancel the 25! on the numerator and denominator for easier solving.)

30P5 = 30x29x28x27x26

30P5 = 17,100,720. It is not the final answer because we can still arrange the 5 winners.

5! = 5*4*3*2*1 = 12017,100,720 * 120 = 2,052,086,400