Question

Of 8 household chores, in how many ways can you do three-fourths of them?

Answer 1

8C6

Answer 2

or for someone who hasnt encountered binomials - "three fourths" of eight is 6

so we are choosing 6 chores, the first choice we have 8 options , then we have 7, etc etc

so (8*7*6*5*4*3) , but then we have counted a bunch of choices more than once,( eg doing the washing up and then the hoovering is the same choice as the hoovering then the washing up_

so we have to divide that number by the different ways to arrange the 6 we chose:

(8*7*6*5*4*3)/(6*5*4*3*2*1)

which is, as experimentX says, 8C6 , which is 28

Answer 3

in general, choosing r objects from a set of n objects there are nCr different possible combinations : nCr = (n!)/(r!(n-r)!)

where the exclamation mark means "factorial"
( basically x! = x*(x-1)*(x-2)*....2*1 , for example 10! = 10*9*8*7*6*5*4*3*2*1 )

Answer 4

N.B 0! = 1

Answer 5

nice job explaining :D
(no choosing 6 places out of 8)/(no of choosing 6 places)