How many words can you make using TATTOO if you have to begin with two T's?

[davidtrinh]

(ex) How many words can you make using TATTOO if you have to begin with two T's?

I try to solve it using combinations.

Consider T T_ _ _ _


The first two positions are saved for the two T's. Now, you can arrange the remaining letters in 4!=24 ways.

But, the answer key says 9.

How do you solve the problem? Thanks for your help.

 

[Steven G]

(ex) How many words can you make using TATTOO if you have to begin with two T's?

I try to solve it using combinations.

Consider T T_ _ _ _


The first two positions are saved for the two T's. Now, you can arrange the remaining letters in 4!=24 ways.

But, the answer key says 9.

How do you solve the problem? Thanks for your help.

Let's look at the 4 letters--T,A,O,O. Don't you think that the fact that there are two O's might affect the answer? Try listing the 24 different ways. How about there being three T's. Will that have any kind of affect?

 

[Steven G]

Hmmm....I get 12 as answer, not 9.

Change the 4 remaining letters to digits:
O's = 1, A = 2 and T = 3
So you have these 12 arrangements:
1 1 2 3
1 1 3 2
1 2 1 3
1 2 3 1
1 3 1 2
1 3 2 1
2 1 1 3
2 1 3 1
2 3 1 1
3 1 1 2
3 1 2 1
3 2 1 1

Oh Sir Jomo, where did I goof, praytell ?

Sir Dennis, I too got 12 (I never said that the answer supplied by the OP was correct!). I did say to try listing the 24 results that the OP thought was the answer.

 

[Steven G]

...and I never said that you said that!

OK, fine. You might be a goof, but you did not goof up your answer.