Discussion
How many 3-digit even numbers can be formed, using the digits 0, 1, 2, 3, 4, 5, if repetition of the digits is allowed :
Answer: A
90 three-digit even numbers can be formed.
With repetition allowed, count the choices for each place. The hundreds digit cannot be 0, so it has 5 choices (1-5). The tens digit can be any of the 6 digits. The units digit must be even, so it has 3 choices (0, 2, 4):
\[ 5 \times 6 \times 3 = 90 \]
216 = 6 × 6 × 6 counts all strings of three digits, including those starting with 0 and odd ones. 150 = 5 × 6 × 5 drops only the leading zero, and 75 does not correspond to a correct count.
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