arragements: 3 yellow, 2 red, 2 blue balloons strung in a row

[2345]

Three identical yellow balloons, two identical red balloons and two identical blue balloons are strung in a row to celebrate Shema's birthday. Calculate the number of arrangements if:
a. the balloon at each end is the same colour.
b. the yellow balloons are next to each other and the blue balloons are not next to each other.

 

[blamocur]

Three identical yellow balloons, two identical red balloons and two identical blue balloons are strung in a row to celebrate Shema's birthday. Calculate the number of arrangements if:
a. the balloon at each end is the same colour.
b. the yellow balloons are next to each other and the blue balloons are not next to each other.

Do you need to satisfy both a) and b) ? Or do you need to solve it separately for a) and separately for b) ?

 

[Dr.Peterson]

Three identical yellow balloons, two identical red balloons and two identical blue balloons are strung in a row to celebrate Shema's birthday. Calculate the number of arrangements if:
a. the balloon at each end is the same colour.
b. the yellow balloons are next to each other and the blue balloons are not next to each other.

Please show us what you have tried, and where you are stuck, as well as what you have learned on this topic. We need to know how we can help you.

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[2345]

Do you need to satisfy both a) and b) ? Or do you need to solve it separately for a) and separately for b) ?

I need to answer both a and b

 

[pka]

I need to answer both a and b

Yes we know that, but you have completely ignored reply #3, why?
Here is the idea needed to solve this problem.
The string of letters Tennessee can be rearranged in [imath]\dfrac{9!}{(4!)([2!]^2)}[/imath] total ways..
Now apply that idea to your string YYYRRBB. You must reply to reply #3!

 

[Dr.Peterson]

Three identical yellow balloons, two identical red balloons and two identical blue balloons are strung in a row to celebrate Shema's birthday. Calculate the number of arrangements if:
a. the balloon at each end is the same colour.
b. the yellow balloons are next to each other and the blue balloons are not next to each other.

For (a), you can consider two or three cases, according to which color is at both ends.

For (b), you can treat the yellow as a single item, and take either an additive or subtractive approach to the problem.

But we really need to see what you know, and what you have tried, in order to give any specific help. We don't give out unearned answers.