OMG WtF!!!?

Question

im doiin math homework
and im doiin combinations

and theres this one problem c[9,2]

i got 1/560


buhh i dont kno
wut u thiink?

thanks babe

Answer 1

You are probably refering to the number of combinations of 9 things taken two at a time. If you understand this concept you would know that 1/560 is impossible.

First learn what the concept means and forget about answers, You want to learn to think, not get a meaningless answer.

Let's find the number of combinations of the letters a,b,c,d taken two at a time. You can easily list them:

ab,ac,ad,bc,bd,cd

Looks like there are only six. You could work your problem the same way but it would take a little time.

The formula for doing this example is

C[4,2] = 4C2 = 4!/[(4-2)!(2!]

= 4x3x2x1/(2x1x2x1 = 6

So you want to calculate

C[9,2] = 9!/[(9-2)!2!] which can be calculated by first

writing = 9x8x7! / [7! x 2!] = 9x8/2x1 = 36

You can also reason the anwer out without formulas if you remember one fact: the number of permutations of n things is n!

We want to find the combinations of 9 things taken 2 at a time

First we get the permutations: there are 9 choices for the first and 8 for the second giving (doing two things in succession)

9 x 8 = 72 permutations.

However two permutations such as ab and ba are just one combination so there are twice the number of permutations as combination. We want combinations so we must divide by 2
C[9,2] = 9 x 8 / 2 = 36.

Grapple with these ideas (list lots of permutations and combinations] and you will be way ahead of those who memorize and get answers but understand nothing.

Answer 2

9C2 = 9!/(7!*2!)
= 9*8/2 = 36