## Related questions with answers

How many positive integers between 100 and 999 inclusive

a) are divisible by 7?

b) are odd?

c) have the same three decimal digits?

d) are not divisible by 4?

e) are divisible by 3 or 4?

f) are not divisible by either 3 or 4?

g) are divisible by 3 but not by 4?

h) are divisible by 3 and 4?

Solution

VerifiedDEFINITIONS

$\textbf{Division rule }$If a finite set $A$ is the union of pairwise disjoint subsets with $d$ elements each, then $n=\dfrac{|A|}{d}$

$\textbf{Product rule }$If one event can occur in $m$ ways AND a second event can occur in $n$ ways, the number of ways the two events can occur in sequence is then $m\cdot n$.

$\textbf{Subtraction rule }$ If an event can occur either in $m$ ways OR in $n$ ways (overlapping), the number of ways the event can occur is then $m+n$ decreased by the number of ways that the event can occur commonly to the two different ways.

$\textbf{Sum rule }$ If an event can occur either in $m$ ways OR in $n$ ways (non-overlapping), the number of ways the event can occur is then $m+n$.

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