Question

A school has five different after-school activities planned in the fall. Kim has time to participate in two of these activities. How many different pairs of after-school activities can Kim chose from the available activities?

Answer 1

hint : number of ways of choosing `k` objects from a collection of `n` objects is
\[\large \binom{n}{k} \]

Answer 2

hint2 :
\[\large \binom{n}{k} = \dfrac{n!}{k!(n-k)!} \]

Answer 3

sorry i am going to try to figure this out really quick haha! i will tag you with the answer i get if that is ok? @ganeshie8

Answer 4

sure :) you're familiar with factorials right ?

Answer 5

yes i am :)

Answer 6

great ! then just plug the numbers and simplify :
n = 5
k = 2

Answer 7

number of ways of choosing `2` objects from a collection of `5` objects is

\[\large \binom{5}{2} = \dfrac{5!}{2!(5-2)!} \]
\[\large = ?\]

Answer 8

ok i got 20??

Answer 9

^^ @ganeshie8

Answer 10

very close, but no - looks you forgot to divide by 2

Answer 11

oh sorry forgot one of the factorials hold on let me work this out

Answer 12

okie

Answer 13

ok i got 10 this time sorry about that :)

Answer 14

10 is \(\large \color{red}{\checkmark }\)

Answer 15

good job !!

Answer 16

Thank you so much

Answer 17

you could have tried this on your own without using the fancy formula as well

Answer 18

wana see how to work this out with out using the formula ?

Answer 19

yeah sure!

Answer 20

also is the formula for a permutation the same as a combination

Answer 21

they look similar, but permutation formula will not have one factorial in the denominator :

\[\large ^nP_r = \dfrac{n!}{(n-r)!}\]

Answer 22

notice that there is not \(\large r!\) in the denominator

Answer 23

oh thank you

Answer 24

check this link when you're free
http://www.mathsisfun.com/combinatorics/combinations-permutations.html

it has excellent explanation for both permutations and combinations

Answer 25

thatk you again this was so helpful

Answer 26

np :)