permutations problem

[margaret.s.chow]

Hello,

I'm having trouble figuring out the following question:

How many different positive integers having six digits are there, where exactly one of the digits is a 3,
exactly two of the digits are a 4, exactly one of the digits is a 5, and each of the other digits is a 7 or an 8?

360
720
840
1,080
1,440

Thanks

[mengnu.liang]

Here is my take:

1) Listing out the numbers 3,4,4,5,7,8 stated in the question

2) Notice that you have two repeating numbers - you need to eliminate that (1,2,3,4,N,N) divide the total possible combination by 2!

3) 6! = total possible combination / 2! = repeated numbers = 360.

Is that the correct answer?

[tim]

close. the wording of the problem allows for 77 or 88 in place of 78. try again, and i'll let you know if it's correct..

[mengnu.liang]

close. the wording of the problem allows for 77 or 88 in place of 78. try again, and i'll let you know if it's correct..

Let me try to rephrase - I forgot to calculate NNNN77 and NNNN88.

Can I just add on 6!/(2!)(2!) = 180 then X 2 = 360

360+360 = 720

Am I even close to what you were referring to?

Thank you very much for your help

[tim]

totally! good job!

[mengnu.liang]

totally! good job!

Thank you very much Tim. Just wondering how would you approach the question. Do you have an easier way to do this type of problems? I wouldn't have gotten it right until you pointed out that I have missed 2 sets of possibilities.

[tim]

no, this is the best way to do this one, you just have to be careful to read the problems and interpret what they're asking for. this is a good skill to develop for CR as well..

[THANU.KG]

Hi,
Quick question on this.
_______
Let me try to rephrase - I forgot to calculate NNNN77 and NNNN88.

Can I just add on 6!/(2!)(2!) = 180 then X 2 = 360

360+360 = 720
_______

On the response above, can you tell me how and why we do * 2 = 360. If it is because we have NNNN77 and NNNN88, then why should we add 360 + 360 = 720.

[mengnu.liang]

Hi,

On the response above, can you tell me how and why we do * 2 = 360. If it is because we have NNNN77 and NNNN88, then why should we add 360 + 360 = 720.

Because the first 3 steps are

1) Listing out the numbers 3,4,4,5,7,8 stated in the question

2) Notice that you have two repeating numbers - you need to eliminate that (1,2,3,4,N,N) divide the total possible combination by 2!

3) 6! = total possible combination / 2! = repeated numbers = 360.

[jnelson0612]

Nice explanation! Thanks everyone!

[THANU.KG]

So it is

3,4,4,5,7,7 --> 6!/(2!) (2!)
+
3,4,4,5,8,8 --> 6!/(2!) (2!)
+
3,4,4,5,7,8 --> 6!/(2!)

= 720?

[tim]

correct!

[THANU.KG]

Got it. Thanks Tim.

[tim]

:)

[amycompton]

The wording of the problem allows for 77 or 88 in place of 78. Try again, and I will let you know if it's correct.