Question

There are 2 black balls, one red ball and one green ball, identical in shape and size. How many different linear arrangements can be generated by arranging these balls?

Answer 1

Answer: The number of different linear arrangements can be generated by arranging these balls is 12.

Step-by-step explanation:

The number of ways to arrange n things in a line where a things are like and b  things are like is $\dfrac{n!}{a!\ b!\ ....}$

Given : There are 2 black balls, one red ball and one green ball, identical in shape and size.

Total balls = 2+1+1=4

Here 2 black balls are alike.

So , the number of different linear arrangements can be generated by arranging these balls would be$\dfrac{4!}{2!}=\dfrac{4\times3\times2!}{2!}=12$

Hence, the number of different linear arrangements can be generated by arranging these balls is 12.