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

Explanation	Calculations	Help
$We first name each digit of the five-digit number.$	$a = ten-thousands digit b = thousands digit c = hundreds digit d = tens digit e = units digit$
$We then count how many choices there are for the first digit. It cannot be zero and must be a multiple of 3.$	$can be 3, 6, or 9\text{options} = 3$$
$Next, we count the choices for each of the remaining four digits. Each can be zero or 3, 6, or 9.$	$can be 0, 3, 6, or 9\text{options for each digit} = 4$$
$We multiply the number of options for each digit since each choice is independent.$	$3 \times 4 \times 4 \times 4 \times 4 = 768$	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 5 digits are multiples of 3 ?

Explanation	Calculations	Help
$We first name each digit of the five-digit number.$	$a = ten-thousands digit b = thousands digit c = hundreds digit d = tens digit e = units digit$
$We then count how many choices there are for the first digit. It cannot be zero and must be a multiple of 3.$	$can be 3, 6, or 9\text{options} = 3$$
$Next, we count the choices for each of the remaining four digits. Each can be zero or 3, 6, or 9.$	$can be 0, 3, 6, or 9\text{options for each digit} = 4$$
$We multiply the number of options for each digit since each choice is independent.$	$3 \times 4 \times 4 \times 4 \times 4 = 768$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

A