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19 Nov 2008, 17:14
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Of the three-digit positive integers that have no digits equal
to zero, how many have two digits that are equal to each
other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216
to zero, how many have two digits that are equal to each
other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216
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19 Nov 2008, 21:01
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Answer: E.
Here is my answer:
we call the number is abc (each has the value from 1 to 9).
we have 9 pairs of number that equal: (1,1);(2,2);(3,3);...;(9,9)
so we have 9 choices for 2 equal numbers, the remaining number has 8 choices(because it's different from the number of 2 equal numbers, forexample if you chose (1,1) then you can chose the remaining number 2,3,...9: 8 choices).so we have 9.8=72 choices for number
Now,the posion for number:
we have 2C3 choices for the position of 2 equal numbers and 1 for the remaining number, then the choices is : 2C3.1.72=3.1.72=216. So E is my choice
Here is my answer:
we call the number is abc (each has the value from 1 to 9).
we have 9 pairs of number that equal: (1,1);(2,2);(3,3);...;(9,9)
so we have 9 choices for 2 equal numbers, the remaining number has 8 choices(because it's different from the number of 2 equal numbers, forexample if you chose (1,1) then you can chose the remaining number 2,3,...9: 8 choices).so we have 9.8=72 choices for number
Now,the posion for number:
we have 2C3 choices for the position of 2 equal numbers and 1 for the remaining number, then the choices is : 2C3.1.72=3.1.72=216. So E is my choice
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
