Help with Combinations!!!!!!
(C(13,4) - (C(7,4)*C(6,4)))/(C(13,4)

Question

Help with Combinations!!!!!!
(C(13,4) - (C(7,4)*C(6,4)))/(C(13,4)

kinggeorge · Answer

Do you know the formula for what C(n,k) is?

anonymous · Answer

n!/((n-r)!r!)

n=13
r=4
=715

n=7
r=4
=35

n=6
r=4
=15

anonymous · Answer

n is the pool or what you are choosing from and k is the select or the amount you can take

kinggeorge · Answer

Basically that's what it it is. But as dreadslicer pointed out above, the formula for C(n,k) is$$C(n,k)=\frac{n!}{k!(n-k)!}$$Using this, you can individually calculate the different values you need. Since you need to find $$\frac{C(13,4)-C(7,4)\cdot C(7,3)}{C(13,4)}$$You need only to find C(13,4), C(7,4), and C(7,3). Can you list these out for me?

anonymous · Answer

(715)-(525)/(715)

kinggeorge · Answer

Looks correct to me. Now you just simplify that as much as you can.

anonymous · Answer

yeah but when i do i get the wrong answer :[

anonymous · Answer

the whole problem is this : Jean-Luc's starship encounters an enemy starship. After realizing that he had no
choice but to get, Jean-Luc orders his weapons ocer to re 4 weapons at the enemy
starship. The weapons ocer randomly selects the 4 weapons to re from a total of
6 photon torpedoes and 7 positron torpedoes. What is the probability that officer
selected torpedoes of both types?

anonymous · Answer

i thought i could take the compliment... did i do it right?

kinggeorge · Answer

You nearly had it. Just instead of multiplying C(7,4) and C(6,4), subtract both of them. So your equation should be $$\frac{C(13,4)-C(7,4)-C(7,3)}{C(13,4)}$$You take out the choices where you choose all positron torpedoes, and then take out the choices where you chose only photon torpedoes. Then you divide by the total.

kinggeorge · Answer

And that should be a C(6,4) not a C(7,3). Sorry about that...

anonymous · Answer

ohhhh you subtract them? i thought i could combine them by multiplying them. is there anyreason as to why i couldnt do that?

kinggeorge · Answer

Basically, you have two cases. Case 1, all positron torpedoes. Case 2, all photon torpedoes. When you have two distinct cases like this, you have to add/subtract.

kinggeorge · Answer

And I've got to go now, feel free to ask more questions as a response, and I'll take a look later tonight.

anonymous · Answer

ok thank you!!!