Question

There are 20 students in a class. Determine how many different pairs you could make out of the class. Be sure to state if the problem involves a permutation or a combination and state if repetition is allowed. Show all of your work and explain your answer.

Answer 1

there are lots of different ways to do this problem
where did it come from? maybe we can pick a good strategy

Answer 2

Its in my combination permutation lesson

Answer 3

ok
i would not imagine using any formula for this

Answer 4

pick a student
how many students can you pair her up with?

Answer 5

Theres alot of ways.. have pairs of 2, 4, 5 & 10

Answer 6

hold on a sec
pick a student
the question is "how may other students can you pair her up with?"

Answer 7

is it clear that there are 19 other students you can pair her up with?

Answer 8

oh yeah

Answer 9

Determine how many different pairs you could make out of the class with 20 students. It dont sday with just 1

Answer 10

i think maybe you have misinterpreted the question, unless i have
pairs mean 2 right? now "how many ways can you divide the class"

Answer 11

yes i know, but we are not done
just getting there

Answer 12

with the first student, there are 19 ways
then there are 18 students left
pick one
there are 17 other students to pair her up with
now there are 16 left
pick one
there are 15 students to pair her up with
etc

Answer 13

by the counting principle, the number of ways to do all of this together is
\[19\times 17\times 15\times 13\times 11\times 9\times 7\times 5\times 3\]

Answer 14

654729075 is what i got

Answer 15

Now what?