How many 4 -digit positive integers are there in which all 4 digits are even?

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500 We first define each digit of the 4-digit number with a variable. a = thousands digit b = hundreds digit c = tens digit d = units digit We then count the possible values for the thousands digit, which cannot be zero for a 4-digit number. a 2,4,6,8 (4 options) We next count the possible values for the hundreds, tens, and units digits, which can include zero. b,c,d 0,2,4,6,8 (5 options each) We multiply the counts for each digit since each choice is independent. 4 5 5 5 = 500

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$We first define each digit of the 4-digit number with a variable.$	$a = thousands digit b = hundreds digit c = tens digit d = units digit$
$We then count the possible values for the thousands digit, which cannot be zero for a 4-digit number.$	$a \in {2, 4, 6, 8} (4 options)$
$We next count the possible values for the hundreds, tens, and units digits, which can include zero.$	$b, c, d \in {0, 2, 4, 6, 8} (5 options each)$
$We multiply the counts for each digit since each choice is independent.$	$4 \times 5 \times 5 \times 5 = 500$

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