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two less than the middle digit

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by sanju09 » Thu Mar 24, 2011 3:00 am
If a three-digit number is selected at random from the integers 100 to 999, inclusive, what is the probability that the first digit and the last digit of the integer will both be exactly two less than the middle digit?
A. 1:900
B. 7:900
C. 9:1000
D. 1:100
E. 7:100


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by manpsingh87 » Thu Mar 24, 2011 3:25 am
sanju09 wrote:If a three-digit number is selected at random from the integers 100 to 999, inclusive, what is the probability that the first digit and the last digit of the integer will both be exactly two less than the middle digit?
A. 1:900
B. 7:900
C. 9:1000
D. 1:100
E. 7:100


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out of 900 number any one can be picked out in 900C1 ways.

also 1 and 3 digit must be same.
therefore, favorable cases are (1,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)
therefore required probability is 7C1/900C1 = 7/900 hence B
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