How many combinations?

How many combinations are possible with 10 initial choices and 5 decisions to make if repetition is allowed?

Let A,B,C,D AND E   al represent different elements of the initial possible 10 sample space.

 

I will say up front that I do not know if this is right but this is my best guess.

 

AAAAA = 10  combinations

 

AAAAB = 10C2*2= 90  combinations           

 

AAABB   = 10C2*2= 90 combinations           

 

AAABC  = 10C3*3=  360 combinations      

 

AABBC   =  10C3*3 = 360 combinations

 

AABCD = 10C4 *4 = 820 combinations

 

ABCDE = 10C5 = 252  combinations

 

So what do I have

 

10+90+90+360+360+820+252 = 1982 combinations