
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 15th, 2018, 09:41 PM  #1 
Senior Member Joined: Apr 2008 Posts: 193 Thanks: 3  How do you do this TATTOO problem?
(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. Then, I divide 24 by 2 because there are two O's. So, my answer is 12. But, the answer key says 9. How do you solve the problem? Thanks for your help. 
June 15th, 2018, 09:53 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,184 Thanks: 481 Math Focus: Calculus/ODEs 
So, we are essentially looking for the permutations of 4 objects, where 2 are identical. I would say: $\displaystyle N=\frac{4!}{2}=12$ I would do it the same way you did. 
June 15th, 2018, 10:18 PM  #3 
Newbie Joined: Jun 2018 From: USA Posts: 2 Thanks: 0 
The word should start with two Ts. Hence the third letter shall be either A or O but not T. Case 1: The third letter be A. Then the remaining 3 can be filled by 3!/2 =3. Case 2: The third letter be O. Then the remaining 3 can be filled by 3!=6. So the total number of words that can be formed is 6+3=9. 
June 15th, 2018, 11:47 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,009 Thanks: 1042 
If the 3rd letter can be a "T" then the answer is 12. If the 3rd letter cannot be a "T" then the answer is 9. It depends on your interpretation of "you have to begin with two T's" I'd say the answer is 12. The arrangement TTTAOO for example does start with 2 T's imo. 
June 16th, 2018, 02:44 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,765 Thanks: 860 
Easier if TAOO = 1233

June 29th, 2018, 09:04 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,244 Thanks: 887 
It's really a question of interpretation. Does "starts with two 't's" mean "starts with exactly two 't's" or "starts with at least two 't's".


Tags 
problem, tattoo 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
tattoo idea  ehh  New Users  19  May 26th, 2013 08:48 PM 
My new tattoo.  FreaKariDunk  New Users  4  September 20th, 2011 11:58 PM 