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How many 4-digit positive integers are there in which each digit is a multiple of 3?

Explanation	Calculations	Help
$We first name each digit of the 4-digit number as a variable.$	$a = thousands digit b = hundreds digit c = tens digit d = units digit$
$We then count the possible values for the thousands digit. It cannot be zero and must be a multiple of three.$	$Choices for a : 3, 6, 9 (3 choices)$
$Next, we count the possible values for each of the other digits. They can be zero or a multiple of three.$	$Choices for b, c, d : 0, 3, 6, 9 (4 choices each)$
$We check that the digit choices are independent and then apply the Combinatorics AND Rule .$	$3 \times 4 \times 4 \times 4 = 192$	Theory & Tactics Method Card PC2-A Click to view full details

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A

How many 4-digit positive integers are there in which each digit is a multiple of 3?

Explanation	Calculations	Help
$We first name each digit of the 4-digit number as a variable.$	$a = thousands digit b = hundreds digit c = tens digit d = units digit$
$We then count the possible values for the thousands digit. It cannot be zero and must be a multiple of three.$	$Choices for a : 3, 6, 9 (3 choices)$
$Next, we count the possible values for each of the other digits. They can be zero or a multiple of three.$	$Choices for b, c, d : 0, 3, 6, 9 (4 choices each)$
$We check that the digit choices are independent and then apply the Combinatorics AND Rule .$	$3 \times 4 \times 4 \times 4 = 192$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

A