Permuations and Combinations

Question

In a row of 6 counters, 3 are red, 2 are blue and 1 is white.
Find the number of arrangements in which no red counter is
next to another red counter. 

Answer 1

Let's show all possible patterns where reds (R) are never adjacent--i.e. they're separated by some other (O).

RORORO ... call this "Leading Red" configuration

OROROR ... call this"Trailing Red configuration.

 

For Leading Red: Since all reds are assumed to look alike, let's put the only white in first or second or third O-position. Then the blues go into whatever unfilled positions remain. So this looks like 3 ways, altogether

 

For Trailing Red:  same remark as above!

 

So it appears that there are 6 possible patterns, half of which begin with R and alternate, and the other half begin with 2nd position Red and alternate THIS ANSWER HAS BEEN EDITED.