Probability using Exclaimation marks! I am lost when it comes to the bigger numbers.

[Gr8fu13]

Question is:
A sales crew has 10 males and 10 females. They need to form a group of 6 people. When choosing at random, what is the probability that the group will consist of 3 males and 3 females?

I know that probability would set the problem up as:

---10!--------- 10!
3!(10-3)! x 3!(10-3)!
---------20!
-----6!(20-6)!

I figured out the top portion using a calculator and the X! button. It would be:

120 x 120
----20!
6!(20-6)!

I cannot fugure out how to calculate the bottom of the problem. I tried 20! on the calculator and it came up with something like 2.432902008^18. I do not know how to incorporate that into the problem. Can someone please assist me? Hope this makes sense. I couldn't get the spaces lined up like I wanted to so I used dashes to line it up. Thanks so much in advance

 

[Deleted member 4993]

Question is:
A sales crew has 10 males and 10 females. They need to form a group of 6 people. When choosing at random, what is the probability that the group will consist of 3 males and 3 females?

I know that probability would set the problem up as:

---10!--------- 10!
3!(10-3)! x 3!(10-3)!
---------20!
-----6!(20-6)!

I figured out the top portion using a calculator and the X! button. It would be:

120 x 120
----20!
6!(20-6)!

I cannot fugure out how to calculate the bottom of the problem. I tried 20! on the calculator and it came up with something like 2.432902008^18. I do not know how to incorporate that into the problem. Can someone please assist me? Hope this makes sense. I couldn't get the spaces lined up like I wanted to so I used dashes to line it up. Thanks so much in advance

That exclamation sign in mathematics is called "factorial". It has following definition:

n! = 1 * 2 * 3 * 4 * ........*(n-3) * (n-2) * (n-1) * n

thus

5! = 1 *2 * 3 * 4 * 5 = 120

Thus:

\(\displaystyle \dfrac{20!}{6! * 14!} \ = \ \dfrac{20*19*18*17*16*15}{6*5*4*3*2*1} \ = \ 19*17*8*15 \ = \ 38760\)

 

[pka]

Some calculators have a combination button \(\displaystyle \boxed{_nC_k}\) or may be \(\displaystyle \boxed{\binom{n}{k}}\).

 

[Gr8fu13]

@Pka- My calculator does not have that key either I suppose I need to invest in a $130.00 one. I have been holding off but I am sure it's well worth it. I have a Texas Instruments-TI-30XA.

@Subhotosh- How do you end up with 19 * 17 * 8 * 15 ? I think once I understand that I will be okay Thanks!

 

[Gr8fu13]

Thank you to everyone for your help!! Sometimes it just takes different wording and examples for me to grasp a concept