permutation

Question

How many 10 letter permutations are possible with the letters{a,a,b,b,b,c,c,c,c},if all the letters are used at a time?

Comments

there are only 9 elements in the set, but you want 10 letter word , it means repetition allowed?

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yes repetion is allowed.

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given that, all the letters are used at a time ===> 9 letters should use

there are three choices to choose the 10th letter

1) choose a ====> $\frac{10!}{3! * 3! * 4!} $ = 4200

2) choose b ====> $\frac{10!}{2! * 4! * 4!} $ = 3150

3) choose c ====> $\frac{10!}{2! * 3! * 5!} $ = 2520

Total = 4200+3150+2520 = 9870

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The question is how many 10 letter permutations are possible with the letters {a, a, b, b, b, c, c, c, c} if all the letters of the set is used at a time. The answer given is 12600. Can anyone explain

Answer 1

as in question all the letters are used at a time and u r telling repetion is allowed in ur comment. so, be clear what is Question.

Comments

The question is given in this manner only and if there are 10 positions and 9 letters than it is well understood that there must be repetition for the 10th place ?correct me if i am wrong.