Cups on the shelf

We should place two green, three red, and two yellow cups side by side on the shelf.
a) How many different ways of setting up can arise?
b) How many different ways of arranging can arise if cups of the same color stand side by side?

Final Answer:

n =  210
b =  6

Step-by-step explanation:

$n=\frac{7!}{2!\cdot 3!\cdot 2!}=210$

$b=3\cdot 2\cdot 1=6$

Try another example