Question

A professor must randomly select 4 students to participate in a mock debate. There are 15 students in his class. In how many different ways can these students be selected, if the order of selection does not matter?

Answer 1

Let's say you had 4 slots: A,B,C,D

how many choices do you have for slot A?

Answer 2

15

Answer 3

how many do you have for slot B?

Answer 4

15

Answer 5

once you pick a person, you cannot pick them again

so you have 15-1 = 14 choices for slot B

Answer 6

how about slot C?

Answer 7

13

Answer 8

and slot D?

Answer 9

omg i get it now thank you

Answer 10

what result do you get

Answer 11

32760

Answer 12

that would be the answer if order mattered

but order does NOT matter

Answer 13

if you had 4 students, call them A,B,C,D

then ABCD is the same as ACBD and ADCB

there are 4! = 4*3*2*1 = 24 ways to rearrange ABCD. So we have to divide by 24 to make the correction

Answer 14

32760/24 = 1,365

Answer 15

there are 1,365 different ways to pick 4 people (order doesn't matter)

Answer 16

oh okay thank you

Answer 17

you're welcome