Question

simplify 15c3

Answer 1

do u know what a factorial is?

Answer 2

no see i didnt pay attention much so thats why i need help

Answer 3

the answer for this question is::
(15!)/((3!)(12!))

Answer 4

where n!=n(n-1)(n-2)(n-3)(n-4).........2.1

Answer 5

n! denotes n factorial

Answer 6

would you mind explaining?

Answer 7

Simplifying:
\[\large 15c^3?\]

Answer 8

sorry i thought c is for combinations/.....

Answer 9

or
\[\large 15c\times 3?\]
or something else like what nitz wrote?

Answer 10

no i think it is
\[_{15}C_3\] known as "15 choose 3" the number of ways you can choose 3 items from a set of 15 items
counting principle gives the answer as
\[\frac{15\times 14\times 13}{3\times 2}\]

Answer 11

idk see on my computer the c shows up on top of the 15 and 3 but it wont let me post it like thsat

Answer 12

yes thats how it is

Answer 13

ok then it is definitely "15 choose 3"\[^{15}C_3\] maybe

Answer 14

yeah but i have no clue how to solve it

Answer 15

you have 15 items and you want to know how many ways there are two choose 3 of them
15 choices for the first
14 choices for the second
13 choices for the third,
then divide by the number of ways you can reorder those three items chosen, which is \(3\times 2=6\)
counting principle tells you it is
\[^{15}C_3=\frac{15\times 14\times 13}{3\times 2}\] can cancel first, multiply last

Answer 16

another example may help
\[^{10}C_4=\frac{10\times 9\times 8\times 7}{4\times 3\times 2}\]

Answer 17

okay thanks!!

Answer 18

btw @nitz answer is the same as the one i wrote, just requires more cancellation

Answer 19

yw

Answer 20

right........but you explained in a better way