Question

How many four digit natural numbers not exceeding the number $4321$ can be formed using the digits $1,2,3,4,$ if repetition is allowed?

Answer 1

The total numbers starting with $1$ is $4\times 4\times 4=64$

Starting with $2$ is $4\times 4\times 4=64$

Starting with $3$ is $4\times 4\times 4=64$

Starting with $44$ is $4\times 4=16$

Now number with $\mathrm{43..}$ given as

$4344$ - $\left(1\right)$

$4343$ - $\left(2\right)$

$4333$ - $\left(3\right)$

$4334$ - $\left(4\right)$

$4323$ - $\left(5\right)$

$4322$ - $\left(6\right)$

$4321$ - $\left(7\right)$

$\therefore$ Total numbers $=64+64+64+16+7$

$=215$.