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How many 5 -digit positive integers are there in which all five digits are multiples of 3 ?

Explanation	Calculations	Help
$We first name the digits of the number as variables.$	$a = ten-thousands digit b = thousands digit c = hundreds digit d = tens digit e = units digit$
$We then count how many choices there are for the ten-thousands digit, which cannot be zero.$	$a = 3, 6, or 9 (3 options)$
$We next count how many choices there are for each of the remaining digits, which may include zero.$	$b, c, d, e = 0, 3, or 9 (4 options each)$
$We multiply the counts for each digit since each choice is independent by Combinatorics AND Rule .$	$3 \times 4 \times 4 \times 4 \times 4 = 768$	Theory & Tactics Method Card PC2-A Click to view full details

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A

How many 5 -digit positive integers are there in which all five digits are multiples of 3 ?

Explanation	Calculations	Help
$We first name the digits of the number as variables.$	$a = ten-thousands digit b = thousands digit c = hundreds digit d = tens digit e = units digit$
$We then count how many choices there are for the ten-thousands digit, which cannot be zero.$	$a = 3, 6, or 9 (3 options)$
$We next count how many choices there are for each of the remaining digits, which may include zero.$	$b, c, d, e = 0, 3, or 9 (4 options each)$
$We multiply the counts for each digit since each choice is independent by Combinatorics AND Rule .$	$3 \times 4 \times 4 \times 4 \times 4 = 768$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

A