Question

*PROBABILITY*

How would you evaluate the number of combinations of 8 things taken 3 at a time?

Answer 1

@ganeshie8 Hey gane, may you try to help with this problem?

Answer 2

familiar with factorial notation ?

Answer 3

No.

Answer 4

basically its a lazy way of writing product of positive integers less than or equal to an integer

Answer 5

for example : \[5! = 5\times 4\times 3\times 2\times 1\]

Answer 6

one more : \[8! = 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\]

Answer 7

so

Answer 8

we have 8C3

Answer 9

So what would C mean

Answer 10

8 would be 1x2x3x4x5x6x7x8, right? and 3 would be 1x2x3?

Answer 11

we have this combination formula\[\large _nC_r = \frac{n!}{(n-r)! r!}\]

Answer 12

plugin the given numbers and work it and yes you're right, you will be using them in the formula :)

Answer 13

\[\large _8C_3 = \frac{8!}{(8-3)! 3!} \]

Answer 14

in nCr,
C can be read as "choose"

Answer 15

what does ! mean

Answer 16

you're basically choosing "r" objects from the available "n" objects

Answer 17

"8!" is read as "8 factorial"

Answer 18

it just means to expand the product till you reach 1 :
\[8! = 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\]

Answer 19

so 8x7x6/3x2x1

Answer 20

Perfect!

Answer 21

so the answer is 56?

Answer 22

Yes! you may use wolfram also. it understands factorials and combinations
http://www.wolframalpha.com/input/?i=8+choose+3

Answer 23

c means choose? :)

Answer 24

Exactly! most math terms define themselves

Answer 25

what does P mean @ganeshie8

Answer 26

@ganeshie8

Answer 27

does it mean permutation?

Answer 28

yes, you may use permutation formula

Answer 29

\[\large _nP_r = \dfrac{n!}{(n-r)!}\]

Answer 30

Why is this question still open?

Answer 31

Unintentionally so. @wio