SOLUTION: the number of three-digit odd numbers with no repeated digits is: A) 280 B) 320 C) 336 D) 360 E) 405

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Question 1123457: the number of three-digit odd numbers with no repeated digits is:
A) 280
B) 320
C) 336
D) 360
E) 405
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) (Show Source):
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(1) The units digit has to be odd: how many choices?

(2) The hundreds digit can't be 0; and it can't be the same as the units digit: how many choices?

(3) The tens digit can't be the same as either the units digit or the hundreds digit: how many choices?

By the fundamental counting principle, the number of 3-digit numbers with the specified restrictions is the product of the numbers of choices for each digit.

Answer by ikleyn(52781) (Show Source):
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.

this number = 8*5 + 7*8*5 = 40 + 280 = 320. First addend 8*5 corresponds to the numbers having one of the digits {1, 3, 5, 7 ,9} as the last (ones) digit and 0 (zero) as the middle digit. Second addend 7*8*5 corresponds to the numbers having one of the digits {1, 3, 5, 7 ,9} as the last (ones) digit; any different non-zero at the middle position and any different from these two non-zero digit at the most-left position.