Question

you have 7 old books and need to schoose 4 to give away how many different groups of 4 books can you make

Answer 1

A

Answer 2

7 choose 4.
Written as nCr or n!/((n-r)!r!)
n = number of choices
r = number of choices retained.

Answer 3

As i said it was a

Answer 4

well at first you have 7 choices but after you choose you only have 6 and after that you would only have 5 and after that only 4 and so on. the equation would be 7 x 6 x 5 x 4 (only four numbers because thats how many in a group.) that's how many different combinations you could make

Answer 5

it is 840

Answer 6

There are 7*6*5*4 = 840 ways to pick 4 books if order mattered

since order doesn't matter, you divide by 4! = 4*3*2*1 = 24 to get 840/24 = 35

So there are 35 ways to pick 4 books where order doesn't matter

Answer 7

The alternative is to use the formula mathmate posted

Answer 8

yeah that would make more sense

Answer 9

I'm really bad at math... I tried plugging in the numbers into the formula and I didn't get the right answer. HELP ME PLEEEEASE!!!!

Answer 10

does my method make sense at all?

Answer 11

Not really.

Answer 12

jim i dont think my way made order matter, if order mattered then their would only be 7 ways to do it

Answer 13

Do you see how I got 7*6*5*4 = 840?

Answer 14

@jim_thompson5910 i dont see why you would divide 840 by 24

Answer 15

Yes i see how you got 840

Answer 16

since order doesn't matter, this means ABCD is the same as ACBD or any rearrangement of the 4 letters

Answer 17

yeah thats why im not dividing it

Answer 18

There are 4! = 4*3*2*1 = 24 ways to arrange the 4 letters (order matters)

So when you calculate 7*6*5*4 = 840, you're counting things like ABCD and ACBD which is overcounting things. Dividing by 24 fixes the overcount

Answer 19

But why would you have to multiply 7*6*5*4

Answer 20

Ooh

Answer 21

You have 7 books to choose from for the first choice

Once you've made that first selection, you have 7-1 = 6 choices left

then after the second selection, you have 7-2 = 5 choices

and finally, for the last selection, you have 7-3 = 4 choices

Answer 22

if you could only choose 4 letters out of 7 a b c d e f g h i then you would pick a random one, one out of 7. then their are only 6, then 5 then 4. their in random order!

Answer 23

Oh my gosh!! I get it! THANK YOU SO MUCH!!! YOU SAVED ME!!!!

Answer 24

you're welcome

Answer 25

okay now it makes sense why you would divide it you just confused me for a sec :)

Answer 26

Where order does not matter we talk about combinations where it does matter permutations.
a quick way to work out combinations is to count down from the Total items ( in this ) case 7) and divide by same number of digits going up from 1

in this case we have 7C4 so thats

7*6*5*4
-------
4*3*2*1

8C3 would be

8*7*6
----
3*2*1