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# Of the three-digit positive integers that have no digits

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Manager
Joined: 06 Nov 2008
Posts: 53
Of the three-digit positive integers that have no digits  [#permalink]

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19 Nov 2008, 17:14
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

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Intern
Joined: 26 Sep 2008
Posts: 19

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19 Nov 2008, 21:01
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

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Re: three integers &nbs [#permalink] 19 Nov 2008, 21:01
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# Of the three-digit positive integers that have no digits

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