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How many choices of 3 burrito toppings are possible if there are 9 toppings to choose from?

Statistics
Tutor: None Selected Time limit: 1 Day

This homework will prepare me for my upcoming Algebra 2 Statistics test.  I must show set up and I can use the functions on my calculator to assist me. I cannot just give the answer. I need to show the set up and I want to understand it. Thank you in advance!  How many choices of 3 burrito toppings are possible if there are 9 toppings to choose from?

Apr 18th, 2015

This a combination problem because order does not matter.

Therefore we use  9C3 = 84

Apr 18th, 2015

Thank you, i did use the 9C3 but I got 504. this is what I did...   9! over (9-3)    = 9 over 6  =  9 times 8 times 7 times 6  over 6+= 504      

Apr 18th, 2015

How did you get to 84 Please?


Apr 18th, 2015

Ok, here's the longer way if you don't use your calculator

9C3 = 9! / (9-3)!3! = 9!/ 6!3! = 84

Can u do factorials on your calculator?

Apr 18th, 2015

Remember the formula for combinations:

nCr = n! / (n-r)!r!

Apr 18th, 2015

yes, I did use my calculator. I divided 9 factorial over 6 into the calculator and got 504. Not sure what I am doing wrong. This will affect the rest of the problems that I am trying to solve.  The next one is How many 5 letter passwords can be made if each letter in the alphabet can be used only once? i got 7,893,600 using my calculator.   I want to tell you how much I appreciate your time in helping me

Apr 18th, 2015

9C3 = 9x8x7x6x5x4x3x2x1 / (6x5x4x3x2x1)(3x2x1) = 9x8x7 / 3x2x1 = 84

Apr 18th, 2015

Ok I got it, now I understand how you get the answer.I forgot to divide it by the 3 times 2.

Apr 18th, 2015

Can you help me with another problem? How many 5 letter passwords can be made if each letter in the alphabet can be used only once? i got 7,893,600 using my calculator.   I want to tell you how much I appreciate your time in helping me.

Apr 18th, 2015

For the password question:

Since each letter can be used only once, then order doesn't matter and we once again use the combination formula

26C5 = 65,780

Apr 18th, 2015

I am checking what I did 

Apr 18th, 2015

Oh, wait a minute. I think I did that one wrong. I think it's a special case permutation, that is solved this way:

26x25x24x23x22 = 7,893,600

So, you got it right!

Apr 18th, 2015

Yeah, because the combination would still allow letters to repeat.

Apr 18th, 2015

Ok , I really understand how you are getting these, but I had a review that my teacher gave the answers to and I have used it to figure out these questions. This question, my teacher said the answer was 8,648,640  ((this isnt part of what I need ,but it is what I am using to do this homework??)) Just trying to figure out what he is asking us to do ..... so  the question he gave us the answer of 8,648,640 was---- For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to choose from , in how many ways can this segment be arranged? 

Apr 18th, 2015

Ok great!


Apr 18th, 2015

Oh, sorry to confuse you but I have to take back my last answer because after reading the question again I think it was a trick question. If you read it LITERALLY it says that you can only use each letter of the alphabet ONCE.

So, that means, 26/ 5 is FIVE with a remainder of one which doesn't count.

So the answer should be FIVE!!!  I think it was a trick question.

Apr 18th, 2015

ok , so no need to verify this last one...I was just asking because I used that example to do one on my homework. 

Apr 18th, 2015

hmmm I am really unsure now. So how is 7,893,600 not right anymore?

Apr 18th, 2015

at first when I read it , I thought it was 5 too

Apr 18th, 2015

yes , it is 5 right?

Apr 18th, 2015

I need to be able to explain it.. I got it by thinking 5 times 5 = 25 with one left over. 

Apr 18th, 2015

are you able to help me with some more questions?

Apr 18th, 2015

Yes, it's five because if you can use each letter ONLY ONCE then the only way to do that is to just divide 26 by 5 which gives you 5 unique password, each with different letters.

Apr 18th, 2015

That really WAS a trick question!

Apr 18th, 2015

Thank You! Can you help me with some more?

Apr 18th, 2015

Yes, the disc jokey answer is correct. I get 8,648,640 too. It's a permutation because order matters. In other words, the order that the songs are played matters.

Apr 18th, 2015

How many ways can you choose a manager and an assistant manager from a 13 person team?  

13C2 .  I got 156  ?

Apr 18th, 2015

No, it's a permutation because order matters. That is to say, you can choose two people but only one can be the manager and one can be the assistant. And you can choose THE SAME TWO people again, only this time the roles are reversed, the guy who was the manager is now the assistant, and vice versa.  Does that make sense?  That's why ORDER MATTERS, in this problem.

So, it's 13P2 = 156    LOL, it's the same answer you got, but you did the combination wrong. 13C2 = 78, not 156.

So, the answer is 156 using PERMUTATION, not combination.

Apr 18th, 2015

so am I right saying that it is 156?

Apr 18th, 2015

ok I understand that it is 13P2 not 13C2

Apr 18th, 2015

Yes, but when you work it out you have to use 13P2 = 156

If you say 13C2, then answer would have been 78

Apr 18th, 2015

Ok, great, you got it now.

Apr 18th, 2015

Just be careful with combinations. If you forget that extra r! in the denominator then you'll be calculating a permutation instead.

Apr 18th, 2015

got it! I think my session is expired , where can i find you for more help. I guess I have to make it official and sign up? but I only want help from you. How do I do this. I have about 8 more to do that I have already worked out. Thanks

Apr 18th, 2015

I was laughing because it was such a coincidence that you got the right answer by miscalculating the combination. I've never seen that before. It just took me by surprise.

Apr 18th, 2015

lol

Apr 18th, 2015

Ok, you can send me a private request to do a problem. I would bid on it. If you accept my bid then I'll do the 8 problems you want. I'll only charge you $5.  Sound fair?

Apr 18th, 2015

It's called inviting a tutor to answer a problem. I'm not exactly how you do that with Studypool. But I get invitations all the time from students and it pops up on my message board as a student has invited me to answer a question.

Apr 18th, 2015

ok thanks :) funny thing is I don't know how I got the 156  neither, but I got it. I have spent so much time working on this because it will probably count as a take home test grade so the teacher expects us to get 100!   and although I have done all of it , I just want to be sure that they are correct.  Just need a little guidance. Going to request that now. thanks

Apr 18th, 2015

you're welcome :)

Apr 18th, 2015

Ok I finally got through it , I see two views although I just sent it to only you I thought. Please check. I will pay you 10 instead of 5 for now. Thanks

Apr 18th, 2015

Ok, I'm going to eat dinner now. I'll check it when I'm done in about 20 minutes. Thanks.

Apr 18th, 2015

No problem , enjoy dinner :)

Apr 18th, 2015

Can we make this chat private. I just noticed that it is not.  I will still be giving you an exceptional rating.

Apr 18th, 2015

I think only you and I can see this conversation.

Apr 18th, 2015

Once you accept my bid we can begin.

Apr 18th, 2015

When I hit to see your reviews the most recent question that I see is mine with the heading burritos and I see the whole chat. Not sure that is good.  Maybe only visible to me? I do know that these questions are now paid and private though. Just wondering if you could go to your reviews later.maybe delete the chat that automatically got on there if it is not private , I would like it to be , thanks. Ok so just so you know , I did accept and just paid :)

Apr 18th, 2015

Yes, I'll do that. I'm working on it now. Thanks.

Apr 18th, 2015

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