Mathematics - Permutation & Combination Question with Solution | TestHub

Given,

Numbers $1,3,5,7,9$

Now to form number between $5000-10000$

$\begin{array}{cccc}\underset{5,7,9}{\underbrace{\_}}& \underset{4 \text{ways}}{\underbrace{\_}}& \underset{3 \text{ways}}{\underbrace{\_}}& \underset{2 \text{ways}}{\underbrace{\_}}\end{array}$

Here at $1000\text{'}\text{s}$ place should be taken by $5, 7 \& 9$

So for $1000\text{'}\text{s}$ place there will be $3$ ways,

Now for hundredth place there will be $4$ ways,

For ten's place there will be $3$ ways,

And for unit place there will be $2$ ways,

So total ways will be $3\times 4\times 3\times 2=72$ ways.