Help..... Simplify the expression. 12P5

Question

hartnn · Answer

$\Large ^nP_r = \dfrac{n!}{(n-r)!}$

hartnn · Answer

here, n = 12, r = 5
plug in values!

yanasidlinskiy · Answer

$$=\frac{ 12! }{ (12-5)! } = \frac{ 12 }{ (7)! }$$
What would I do after that?

hartnn · Answer

you know how n! gets calculated ?

yanasidlinskiy · Answer

umm...idk..

hartnn · Answer

$\Large n! = n \times (n-1)\times (n-2)\times ... 3 \times 2\times 1 \ eg:  4! = 4\times 3\times 2\times 1$

anonymous · Answer

7!=7*6*5*4*3*2*1

hartnn · Answer

another example : 
$7! = 7 \times 6\times 5\times 4\times 3\times 2\times 1$

hartnn · Answer

oh and the numerator is 12! isn't it ?

hartnn · Answer

$=\frac{ 12! }{ (12-5)! } = \frac{ 12! }{ (7)! }$

yanasidlinskiy · Answer

Yes. It is.  I am going to solve this and you tell me if I'm right. Ok?

hartnn · Answer

sure

yanasidlinskiy · Answer

$$\frac{ 12*11*10*9*8*7*6*5*4*3*2*1 }{ 7*6*5*4*3*2*1 }=95,040$$ Am i right?

hartnn · Answer

thats absolutely correct! :)

yanasidlinskiy · Answer

Yay!!:) Wow...So proud....When I submit...my exam...I will tell you what score i got!!:) lol!!

hartnn · Answer

here's a neat trick to do these faster, say we have 6! / 3! 

we know that
3! = 3.2.1
and  6! = 6.5.4.3.2.1 
see anything common ?
yes! 3.2.1

so, 6! = 6.5.4.3! 
so, 6!/3!  is just 6.5.4  :)

hartnn · Answer

similarly, your 12!/ 7! will simply be 12.11.10.9.8

yanasidlinskiy · Answer

Wait.....I have one more question.....
A number cube is rolled with these results: 64 ones, 67 twos, 73 threes, 59 fours, 72 fives, and 71 sixes. What is the experimental probability of rolling an even number? 

Write your answer as a percent, to the nearest tenth of a percent.
  A. 51.9% 	
  B. 48.5% 	
  C. 53.6% 	
  D. 46.8%

yanasidlinskiy · Answer

Nice!:) Helps e a lot....on my second question i think it would be either B or D.

hartnn · Answer

Experimental Probability = favorable events/ total events = (# of rolls producing even numbers)/ (Total # of rolls)

Total # of rolls = 64+67+...+71 =...

for # of rolls producing even numbers, you consider , 2,4,6 only
 = 67+59+71 = ...

then just divide :)

yanasidlinskiy · Answer

So i would add them before i divide...right?

hartnn · Answer

yesss

hartnn · Answer

see if you get 0.485 , which is 48/5% :)

hartnn · Answer

**48.5 %

yanasidlinskiy · Answer

Um...ok. no. i got like 33.833..I added 67, 64...etc and then added 2,4,6...seperately..then i divided 406 by 12..Thanks for your help though..

yanasidlinskiy · Answer

I got a 100% on my probability test!!!:)