Answer
The number of 4-digit odd numbers less than 6000 that can be formed is\[48\].
Work Step by Step
The number of 4-digit odd numbers less than 6000 that can be formed can be calculated by multiplying the possibility of numbers at each place.
If a number is selected for the first place, then there are 2 ways to select as the number must be less than 6. The number of 2nd and 3rd place can be computed in\[_{4}{{P}_{2}}\]ways. Similarly for the 4th place there are 2 possibilities.
Compute the number of 4-digit odd numbers less than 6000 that can be formed using the equation as shown below:
\[\begin{align}
& \text{Number of 4-digit odd numbers less than 6000}=\text{First place}\times \text{second place} \\
& \times \text{third place}\times \text{fourth place} \\
& =2{{\times }_{4}}{{P}_{2}}\times 2 \\
& =2\times \frac{4!}{\left( 4-2 \right)!}\times 2 \\
& =4\times \frac{4\times 3\times 2!}{2!} \\
& =48
\end{align}\]
