Five-digit 80104

How many different five-digit numbers with different digits can be made from the digits 0, 2, 4, 6, 7, 8, and 9? How many of them are divisible by 4? How many of them are divisible by 10? How many of them are even?

Correct answer:

a =  2160
b =  840
c =  360
d =  1560

Step-by-step explanation:

$a=6\cdot 6\cdot 5\cdot 4\cdot 3=2160$

$$\begin{gathered} XXX04 \\ XXX08 \\ XXX20 \\ XXX24 \\ XXX28 \\ XXX40 \\ XXX48 \\ XXX60 \\ XXX64 \\ XXX68 \\ XXX72 \\ XXX76 \\ XXX80 \\ XXX84 \\ XXX92 \\ XXX96 \\ b=(5\cdot 4\cdot 3)\cdot 6+(4\cdot 4\cdot 3)\cdot 10=840 \end{gathered}$$

$c=6\cdot 5\cdot 4\cdot 3\cdot 1=360$

$d=6\cdot 5\cdot 4\cdot 3\cdot 1+5\cdot 5\cdot 4\cdot 3\cdot 4=1560$

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