You own 7 books and are taking 5, how many ways can you choose which books to take?

Answer is 21, how do I get there?

Question

You own 7 books and are taking 5, how many ways can you choose which books to take?

Answer is 21, how do I get there?

cwrw238 · Answer

this is the number of combination of 5 from 7  which is the same as number combinations of 2 (7-5) from 7
and is 

7*6
---  = 21
2* 2

cwrw238 · Answer

sorry the denominator is 2*1

anonymous · Answer

K, I was going 5 4 3 2 1 Thanks.

anonymous · Answer

nPr = $$n! \over (n - r)!$$
$$7! \over (7 - 5)!$$
$$7! \over 2!$$
$$7 * 6*5*4*3 $$

cwrw238 · Answer

the maths textbooks give the formula
    n!
------
(n-r)! r!

which simplifies to the way i stated

anonymous · Answer

2520 :0

anonymous · Answer

Thanks to everyone, really. :)

cwrw238 · Answer

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

anonymous · Answer

@cwrw238 Isn't this a permutation because the books aren't being replaced?

cwrw238 · Answer

hhmm - not sure to be honest - now you mention it

anonymous · Answer

Yeah. I think it is. In that case the formula is
$$n! \over (n - r)!$$