The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ________.

Question

Smart Achievers · Accepted Answer

(52)

The units place must be either 0, 4 or 6 for the number to be even.

$\begin{matrix} ↓ & ↓ & ↓ \\ 4 & 5 & 3 \end{matrix} \begin{matrix} \leftarrow No. of ways \end{matrix}$

Number of 3-digit numbers which are even

$= 4 \times 5 \times 3 = 60$

But this includes even numbers with 0 at the hundreds place.

Number of such numbers $= 2 \times 4 = 8$

$∴$ Required number of 3-digit even numbers $= 60 - 8 = 52$

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