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# counting question

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There are six clearly distinguishable frogs sitting in a row. Two are green, two are red, and two are blue. Green frogs refuse to sit next to the red frogs, for they are highly poisonous. In how many ways can the frogs be arranged?

Dec 25, 2020

#1
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I'll walk you through my solution without giving you the final answer.

Let RR sit together

If they are in the 1st and 2nd position how many ways can the there frogs be seated?

If they are in the 2ndand 3rd position how many ways can the there frogs be seated?

If they are in the 3rd and 4th position how many ways can the there frogs be seated?

If they are in the 4th and 5th position how many ways can the there frogs be seated?

If they are in the 5th and 6th position how many ways can the there frogs be seated?

Let there be just one seat between the 2 read frogs

Go through the same process as above.  Look at each alternative.

Do the same for  2 seats between the two red frogs.

3 seats between

4 seats between

and lastly 5 seats between.

Now add the numbers all up.

Dec 26, 2020