anonymous
  • anonymous
Help with Combinations!!!!!! (C(13,4) - (C(7,4)*C(6,4)))/(C(13,4)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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KingGeorge
  • KingGeorge
Do you know the formula for what C(n,k) is?
anonymous
  • anonymous
n!/((n-r)!r!) n=13 r=4 =715 n=7 r=4 =35 n=6 r=4 =15
anonymous
  • anonymous
n is the pool or what you are choosing from and k is the select or the amount you can take

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KingGeorge
  • KingGeorge
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
  • anonymous
(715)-(525)/(715)
KingGeorge
  • KingGeorge
Looks correct to me. Now you just simplify that as much as you can.
anonymous
  • anonymous
yeah but when i do i get the wrong answer :[
anonymous
  • anonymous
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
  • anonymous
i thought i could take the compliment... did i do it right?
KingGeorge
  • KingGeorge
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
  • KingGeorge
And that should be a C(6,4) not a C(7,3). Sorry about that...
anonymous
  • anonymous
ohhhh you subtract them? i thought i could combine them by multiplying them. is there anyreason as to why i couldnt do that?
KingGeorge
  • KingGeorge
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
  • KingGeorge
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
  • anonymous
ok thank you!!!

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