How Many 3-Letter Arrangements of aabbcccdddd Are Possible?

[ashi_mashi]

hi everyone...
how many arrangements of this word "aabbcccdddd" is possible if we only use 3 of them? I know if we could use all of them it would just be 11!/(2!2!3!4!), but what if we only use 3?

Thanks in advance

 

[BicycleTree]

I assume you mean 3 letters in the arrangement. First count the number of ways to permute using 1 letter of each, then in addition to that count the number of ways to permute using 1 of one letter and 2 of another, and then add 2 for the arrangements ccc and ddd.

 

[ashi_mashi]

ok..thanks...so the answer would be 52?

 

[BicycleTree]

Not quite what I got--maybe you added wrong at the end?

 

[ashi_mashi]

umm...i tried it again...i got 62 (checked it 3 times!)

 

[BicycleTree]

Yep, 62 is what I got. You said 52 the other time.

 

[ashi_mashi]

thanks a lot