Cups on the shelf

2 green, 3 red and 2 yellow cups should be placed 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?

Correct answer:

n =  210
b =  6

Step-by-step explanation:

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

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

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