yet another probability question

[xylashellx]

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hello everyone...just when i thought i got the other prob. question on here i take the topscore and get this one...

A flourist purchases three yellow roses, two pink roses, and five red roses. How many three rose arrangements are possible?

the answer is 120.

I think its 10!/3!*7! or something. im sure this can be explained very easily. thanks in advance people!!

 

[ddsnp]

hello everyone...just when i thought i got the other prob. question on here i take the topscore and get this one...

A flourist purchases three yellow roses, two pink roses, and five red roses. How many three rose arrangements are possible?

the answer is 120.

I think its 10!/3!*7! or something. im sure this can be explained very easily. thanks in advance people!!

I'm no math wiz but this is how i learned to do these.


For this question you know that order does not matter so you can use the equation that you had.

it is 10!/3!*7!
which is basically HOw many total number of flowers/(the amount of different combinations that you want, in our case 3)*(Total number of flowers -the amount we want (3))
Then its just simple math

10*9*8*7*6*5*4*3*2*1
-------------------------
3*2*1 * 7*6*5*4*3*2*1

you are left with

10*9*8
-------
3*2*1

then you simplify

10*3*4
-------
1

and you get

30*4
=120

Thats how i do it. Hope it helps.

 

[naithgirw]

Seriously - I heard Probability questions are Overated in terms of Chances of seeing them on the ACTUALL DAT - am I right - please verify this!

 

[xylashellx]

thanks ddsnp,

how would the problem be solved if order did matter?

 

[kew]

A real fast way of doing these problems is take the total number of things in question like this one is 10 for instance. Then take what they actually want and that is 3 things. The fast way I do this is take the 3 biggest numbers multiplied together (10*9*8) divided by the 3 smallest numbers multiplied together (1*2*3). I always just say in my head "OK, 3 in from the top divided by 3 in from the bottom. This equals 120.

 

[cdpiano27]

This question is really very easy. You did not have to no ANYTHING about whether the roses are pink, red, or yellow. To find the number of three rose combinations this has ABSOLUTELY NOTHING to do with the colors.
It is simply choosing any three roses out of a possible 10. And we do not care about order so simply 10 nCr 3.

However, a question more specific than this could be asked. Let us say we could be have a question worded as the following:

Draw four roses.
Out of these four roses,
What is the probability that 2 are pink, 1 is red, and 1 is yellow?

Now the denominator is the number of possible combinations of 4 roses. That is 10 nCr 4 (10 choose 4) (remember this is NOT nPr order has nothing to do with the question!)

Now, we have 3 yellow, 2 pink, and 5 red.
To determine the numerator:
1. Choose 1 out of three yellow roses (3 nCr 1)
2. Choose 1 out of 5 red roses (5 nCr 1)
3. Choose 2 out of 2 pink roses (2 nCr 2)

Now we need use the multiplicative rule since we need the intersection of these three probabilities.

so we have

[(3 nCr1) * (5 nCr 1) * (2 nCr 2)] / (10 nCr 4)
= 15 / [ (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) ]
15 / 210 = 5 / 70 = 1 / 14.


Well, my major is in statistics through masters degree, but the questions on the quantitative will be no harder than your introductory undergraduate statistics class probably the one without calculus. This type of question is probably as hard as it would get. I am sure no statistics questions about randomized block design, one-way or two-way ANOVA, etc, mgf's or probability questions involving a lot of calculus such as finding the probability by integrating multiple times over a certain density function.

Good luck on the quantitative section!

 

[SpikeyMike83]

i totally just got done taking that exact topscore test. I was running out of time so I guessed on that one, but I don't remember what I put. I'll have to look at my score report later. Good to know how to do it now though!