Question

In a baking competition between ten bakers, how many ways is it possible for the top three places, (1st -2nd - 3rd place) to be determined?

In a class of twenty students, how many ways are there to choose two students to participate in a debate?

Answer 1

(A) We have 10 bakers and we have to find the number of ways to select the top three places.

This is a simple permutation problem because order is important and no replacement is allowed. In this case, we have total number of bakers n = 10 and we have to select top three places, so r = 3

Using the formula

Permutation(n,r) = Permutation(10,3) =

we can write 10! as 10*9*8*7!

So, there are 720 different ways to select top three bakers

(B) We have to find the number of ways to choose two students to participate in a debate out of 20 students.

This is a simple combination problem. In this case, we have total number of students n = 20 and we have to select two students, so r = 2

Using the formula

Combination(n,r) = combination(20,2) =

we can write 20! as 20*19*18!

so, we get

Combination(20,2)= (20*19*18!)/(18!*2!) = (20*19)/(2*1) = 380/2 = 190 ways

So, there are 190 ways to select two students out of 20