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How many 5 -digit positive integers are there in which all 5 digits are odd?

Explanation	Calculations	Help
$We first name the digits of the five-digit number.$	$a = ten-thousands digit b = thousands digit c = hundreds digit d = tens digit e = units digit$
$We then find how many choices a has. Since it must be an odd digit and nonzero, there are five possibilities.$	$a can be 1, 3, 5, 7, 9 Number of options for a : 5$
$Each of the other digits b, c, d, and e must also be odd, so each has five possibilities.$	$b, c, d, e can each be 1, 3, 5, 7, 9 Number of options for each: 5$
$Because each digit choice is independent, we apply Combinatorics AND Rule to find the total count.$	$5 \times 5 \times 5 \times 5 \times 5 = 3125$	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 odd?

Explanation	Calculations	Help
$We first name the digits of the five-digit number.$	$a = ten-thousands digit b = thousands digit c = hundreds digit d = tens digit e = units digit$
$We then find how many choices a has. Since it must be an odd digit and nonzero, there are five possibilities.$	$a can be 1, 3, 5, 7, 9 Number of options for a : 5$
$Each of the other digits b, c, d, and e must also be odd, so each has five possibilities.$	$b, c, d, e can each be 1, 3, 5, 7, 9 Number of options for each: 5$
$Because each digit choice is independent, we apply Combinatorics AND Rule to find the total count.$	$5 \times 5 \times 5 \times 5 \times 5 = 3125$	Theory & Tactics Method Card PC2-A Click to view full details

Scroll horizontally to view all columns

A