Question 87331
<pre><b>
How many ways can 12 people out of 300 be selected for a jury?

This is the combinations of 300 things taken 12 at a time.

This is sometimes written C(300,12) and sometimes <sub>300</sub>C<sub>12</sub>

Checkley's answer is wrong as he thought it was permutations,
but because the order of the members of a jury is not important,
we must use combinations, not permutations, which means we 
must divide his answer by 12! or 12·11·10·9·8·7·6·5·4·3·2·1 =
479001600.

So Checkley should have had

 300*299*298*297*296*295*294*293*292*291*290*289     4.252707522E29
------------------------------------------------- = ----------------- =
          12*11*10*9*8*7*6*5*4*3*2*1                    479001600


 4.252707522 × 10<sup>29</sup>
--------------------- = 8.878274148 × 10<sup>20</sup> 
       479001600

Here is how to do it on a TI-83 or TI-84 calculator:

Type in 300
Press MATH
Press <font face = "wingdings 3">|</font> 
Press 3       (You should see this on the main screen: 300 <font face = "lucida console">nCr</font>
Type in 12      (You should see this on the main screen: 300 <font face = "lucida console">nCr</font> 12
Press ENTER

Read this:  8.878274148E20

This means 8.878274148 × 10<sup>20</sup>

or about 

887,827,414,800,000,000,000

887 quintillion, 827 quadrillion, 414 trillion, 800 billion

Edwin</pre>