SOLUTION: 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. The answer given is 12

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Question 1063939: 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.

The answer given is 12. Can you draw boxes and explain it to me?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
I just solved this one this morning:
https://www.algebra.com/algebra/homework/playground/test.faq.question.1063942.html

Basically, you have _B_B_W_ where the _ are spaces for the Red, so 4C3 selections.
However, the BBW also can be re-arranged in 3 ways because there are 3C1 spaces to place W: BBW, BWB, and WBB
Hence, for each of the 4 arrangements of the Red ones, there are 3 arrangements for W so 4x3 = 12.