Question

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 articles for publication?

Answer 1

you are asked to compute the number of ways to choose 9 out of 14
this is written as \(\dbinom{14}{9}\) read "14 choose 9" and computed via
\[\frac{14\times 13\times 12\times 11\times 10}{5\times 4\times 3\times 2}\] cancel first, multiply last
although this button is probably on your calculator

Answer 2

ok so what do you mean by cancel first and multiply last

Answer 3

i mean the answer is a whole number so cancel as must as you can and you will be left only with a multiplication at the end, no division

Answer 4

for example \(5\times 2=10,3\times 4=12\) so this one becomes
\[14\times 13\times 11\]

Answer 5

I still don't understand? Can you show me step by step

Answer 6

you can also just cheat
http://www.wolframalpha.com/input/?i=14+choose+9

Answer 7

do you understand how i got
\[\frac{14\times 13\times 12\times 11\times 10}{5\times 4\times 3\times 2}\]?

Answer 8

nope

Answer 9

ok then that is where we have to start

Answer 10

you are asked how many ways you can choose 9 out of 14

it is easier to answer the question how many ways to choose 5 out of 14

these are obviously the same number, because choosing 9 out of 14 to publish it identical to choosing 5 out of 14 not to publish

Answer 11

in the numerator i start with 14 and count down until i have 5 numbers
that is why the numerator is \[14\times 13\times 12\times 11\times 10\]

Answer 12

ok im with you

Answer 13

ohh ok i understand it now thank you so much

Answer 14

that is like saying
14 choices for the first article
13 choices for the second
12 choices for the third
11 choices for the fourth
10 choices for the fifth

Answer 15

and if "order counted" you would be done at this step
but order does not count in this problem, so i have overcounted by the number of ways i can arrange those 5 articles, which is \(5!=5\times 4\times 3\times 2\)

Answer 16

that is why the answer is
\[\frac{14\times 13\times 12\times 11\times 10}{5\times 4\times 3\times 2}\]

Answer 17

yep and the final answer is 2,002

Answer 18

yes it is
if you are on a computer you can do what i did in the link above
if not, most calculators have a button for this, you can probably find it if you look, or ask someone

Answer 19

ok thank you so much @satellite73

Answer 20

yw