Permutation problem

[Mstoothlady2012]

Can someone plz break this problem down for me & explain it to me in a very basic way. I am very bad at permutations & combination. Thank you!

A jeweler has exactly six distinct beads: 3 agate beads and 3 quartz beads. All the beads are different color. If the jeweler wants to alternate the beads so that no 2 agate or quartz beads are adjacent, in how many different ways could the jeweler string the beads on a single thread?

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[baedero1]

3! * 4P3 = 144

? a ? a ? a ?

or

? b ? b ? b ?

 

[Mstoothlady2012]

3! * 4P3 = 144

? a ? a ? a ?

or

? b ? b ? b ?

that's not the right answer

 

[igotshoe]

Can someone plz break this problem down for me & explain it to me in a very basic way. I am very bad at permutations & combination. Thank you!

A jeweler has exactly six distinct beads: 3 agate beads and 3 quartz beads. All the beads are different color. If the jeweler wants to alternate the beads so that no 2 agate or quartz beads are adjacent, in how many different ways could the jeweler string the beads on a single thread?

i do believe its 72, however im not great explaining permutations so take this for what it is. 6 choices initially * 3 choices for 2nd type of bead * 2 choices of 1st type * 2 choices of 2nd type * 1 choice of 1st type * 1 choice of 2nd type = 6*3*2*2*1*1 = 72

 

[Mstoothlady2012]

i do believe its 72, however im not great explaining permutations so take this for what it is. 6 choices initially * 3 choices for 2nd type of bead * 2 choices of 1st type * 2 choices of 2nd type * 1 choice of 1st type * 1 choice of 2nd type = 6*3*2*2*1*1 = 72

why didnt you multiply 3 choices for 1st type of bead?

 

[iverson3504]

why didnt you multiply 3 choices for 1st type of bead?

because it does not matter which type of bead you start with, therefore you have 6 choices total..

was that the correct answer?

 

[Mstoothlady2012]

because it does not matter which type of bead you start with, therefore you have 6 choices total..

was that the correct answer?

yea nice job. I understand this method better than what Kaplan showed. Thanks!

 

[harrygt]

The correect answer is 72.
Let's say quartz = q
agate = a
In order to get that order, you gotta have either a,q,a,q,a,q or q,a,q,a,q,a

in the first type: there are 3 possibilites for the 'a' on the left, then 2 for the one in the middle [you subtract one, because they can't repeat], and 1 for the 'a' on the right. The same for q. The one on the left has 3 possibilites, then 2 in the middle, and 1 for the q at the right side.
So we have 3 * 3 * 2 * 2 * 1 * 1 = 36.

for the q,a,q,a,q,a situation, you get another 36 ways by the same procedure as I described.

36 + 36 = 72 total ways to make that necklace or whatever.

 

[Mstoothlady2012]

The correect answer is 72.
Let's say quartz = q
agate = a
In order to get that order, you gotta have either a,q,a,q,a,q or q,a,q,a,q,a

in the first type: there are 3 possibilites for the 'a' on the left, then 2 for the one in the middle [you subtract one, because they can't repeat], and 1 for the 'a' on the right. The same for q. The one on the left has 3 possibilites, then 2 in the middle, and 1 for the q at the right side.
So we have 3 * 3 * 2 * 2 * 1 * 1 = 36.

for the q,a,q,a,q,a situation, you get another 36 ways by the same procedure as I described.

36 + 36 = 72 total ways to make that necklace or whatever.

You are gooodd!!! These permutations are gonna mess up my QR score

 

[harrygt]

You are gooodd!!! These permutations are gonna mess up my QR score

I guess there is only one or at most 2 of these questions on the QR.
Lol, I did a lot of these type of annoying question in my 8th grade in an AP math class, and that is why I'm good at those. You can still get better with reading the practice tests' manual. This one was a bit tough. The chances of getting one similar to the one you just posted is much more. I mean the ones you have a few types of stuff in the bag, and you take out some of them at once. Try to learn that for sure.

 

[Mstoothlady2012]

I guess there is only one or at most 2 of these questions on the QR.
Lol, I did a lot of these type of annoying question in my 8th grade in an AP math class, and that is why I'm good at those. You can still get better with reading the practice tests' manual. This one was a bit tough. The chances of getting one similar to the one you just posted is much more. I mean the ones you have a few types of stuff in the bag, and you take out some of them at once. Try to learn that for sure.

This was nothing compared to the other ones that kaplan has in their freaking quizzes. It is so annoying when I can't solve a math problem.