Color Permutations In Row Of 6 Red, 3 Blue, 3 Green Flower Pots ?

[morrobay]

With 6 red, 3 blue and 3 green flower pots, how many color permutations in row of 12 are there ?
Its not 12! or n!/(n-r)!

 

[Number Nine]

Why not try choosing in which places to put the red pots, then choosing which of the remaining places will have blue pots, etc...

 

[morrobay]

I am looking for the formula for this question . It would take a long time to physically determine the answer !
For example 12! ( the number of permutations of a row of twelve jurors is 479, 001,600. How long would that take you to get 12! physically ?
One permutation of the twelve colored flower pots would be :BBRGBGRRGRRR

 

[Char. Limit]

Keep in mind that for permutations with three types of objects, the general formula is:

[tex]P = \frac{n!}{k_1 ! k_2 ! k_3 !}[/tex]

Where n is the total number of objects (12 balls in this case), and [itex]k_1[/itex], [itex]k_2[/itex], and [itex]k_3[/itex] are the number of each type of ball (6 red, 3 blue, and 2 green in this case). Knowing that, you should be able to get the final answer easily.

 

[CellCoree]

The number of color permutations in a row of 12 flower pots with 6 red, 3 blue, and 3 green pots can be calculated using the formula for permutations with repetition. This formula is given by n!/(n1! * n2! * ... * nk!), where n is the total number of items, and n1, n2, etc. are the number of items of each type.

In this case, n=12, n1=6, n2=3, and n3=3. Plugging these values into the formula, we get:

12!/(6! * 3! * 3!) = 12!/216 = 27,720

Therefore, there are 27,720 possible color permutations in a row of 12 flower pots with 6 red, 3 blue, and 3 green pots.