Question

How do I calculate this? "A mathematics journal has accepted 14 articles for publication. However, due to budgetary restraints only 9 articles can be published this month. How many ways can the journal editor assemble 9 of the 14 articles for publication?" I don't fully understand the question. Can someone please explain? Thank you

Answer 1

You have to consider the possibilities. There are are 9 spots and 14 articles. It all has to do with the different ways you can choose the articles. For the first article you have 14 choices, then the second you have 13. So on and so forth. So you multiply 14*13*12*11*10*9*8*7*6. You multiply because then you can count all possible combinations.

Answer 2

@knowledge you just confused me sooo much

Answer 3

When I multiplied that though, I got 726,485,760

Answer 4

@knowledge

Answer 5

14 x 9 = 126... is that not correct?

Answer 6

I am assuming that the order of the articles matters over here. Thus, this kind of ordering of things where order matters is called a permutation. Now I am also assuming that none of the articles are the same, identical pieces of work (lol). With these two assumptions, the formula for the permutations without repetitions is \[\frac{ n! }{ (n-r)! }\] where there are n available things and r things to choose from. In this case there are 14 articles available, but only nine are chosen. Thus,\[\frac{ 14! }{ (14-9)! }\] then, \[\frac{ 14! }{ 5! }\]