+18 I have this question on a study guide, could someone help? 4. A bookstore has a sale and you want to buy cookbooks. They have 12 cookbooks and you decide to buy 3 of them. How many possible combinations could you choose from? I think it's 12!/(12-3)! but im not sure...
It is 12
C
3 that is (12x11x10)/(3x2x1)
because
number of choices for first book =12 which leaves
number of choices for 2nd book=11 which leaves
number of choices for 3rd book =10. With each of your first choices of 12 you then have another 11 choices to make which is 12x11,and with each of those you have another 10,giving you 12x11x10 choices. BUT !!!! -- you aren't finished yet,because within that number of 12x11x10 choices,you will have picked the same bunch of books more than once. For example if you picked books (call them books 1,2 and 3) you will also have picked 132, 213,231,312,321,which are all the same bunch of books. That is you will have picked the same bunch (called a combination) of 3 books six times. So you need to divide the number of choices by the number of ways (called permutations) you can arrange each choice. Which is six.
A combination is a collection of objects (like your bunch of 3 books),a permutation is the number of ways you can arrange those objects.
+37084 I think it is nCr 12 C 3 = 220
You have nPr 12 P 3 = 1320
I am not real strong in this topic though.....
http://www.calculatorsoup.com/calculators/discretemathematics/combinations.php
It is 12
C
3 that is (12x11x10)/(3x2x1)
because
number of choices for first book =12 which leaves
number of choices for 2nd book=11 which leaves
number of choices for 3rd book =10. With each of your first choices of 12 you then have another 11 choices to make which is 12x11,and with each of those you have another 10,giving you 12x11x10 choices. BUT !!!! -- you aren't finished yet,because within that number of 12x11x10 choices,you will have picked the same bunch of books more than once. For example if you picked books (call them books 1,2 and 3) you will also have picked 132, 213,231,312,321,which are all the same bunch of books. That is you will have picked the same bunch (called a combination) of 3 books six times. So you need to divide the number of choices by the number of ways (called permutations) you can arrange each choice. Which is six.
A combination is a collection of objects (like your bunch of 3 books),a permutation is the number of ways you can arrange those objects.
