SOLUTION: How many three digit numbers can be made using only the digits 1 to 9 so that at least two of the digits are the same? For example, 112 and 737 are two such numbers. (A) 100 (B)

Question 206744: How many three digit numbers can be made using only the digits 1 to 9 so that at least two of the digits are the same? For example, 112 and 737 are two such numbers.
(A) 100 (B) 200 (C) 216 (D) 225 (E) None of these
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How many three digit numbers can be made using only the digits 1 to 9 so that at least two of the digits are the same? For example, 112 and 737 are two such numbers.
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# with >= 2 the same = (total # of 3 digit numbers) - (number with no repeats)
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# of 3 digit with no restrictions = 9^3
# of 3 digit with no repeats = 9*8*7 =
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So, # with >= 2 the same = 9^3-9*8*7 = 9(9^2-56)= 9(25) = 225
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Cheers,
Stan H.
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(A) 100 (B) 200 (C) 216 (D) 225 (E) None of these
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