Different color combination of identical balls

Question

There are three identical red balls and four identical blue balls in bag.Three balls are drawn.what is the number of different color combinations ?

Answer 1

Color combination will be 4

(B,B,B),

(B,B,R) 

(R,R,B) 

(R,R,R)

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Another way 

$x_{1}+x_{2}=3$

$\Rightarrow \binom{3+2-1}{2-1}=\binom{4}{1}=4$

 

Comments

Can we generalize it for ,say n one type and m another type identical balls .r balls are drawn.what is the number of different type combinations?

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It is asking for combination - So, RBR = RRB = BRR.

Answer 2

There are 2 types of colors. 1st place can be filled with any of 2 colors, similarly 2nd place with 2 colors and 3rd place with 2 colors . So in total 2 * 2 * 2. Here the order of color doesn't matter as they are asking for combination(i.e.- (RBR) is same as (BRR)).So removing their permutation 8 / 2! = 4  For, say n different type of identical balls where c1,c2....cn are number of balls of 1 color respectively  ,r balls are drawn, number of color combinations will be( r^n)/r! and if order matters then r ^n  provided c1,c2....cn >= r

Comments

Is it not n^r/n! ?

Where n is number of different colors and r is the number of balls drawn.