Question

Consider all the 5 digit numbers where each of the digits is chosen from the set {1,2,3,4}. The number which contain all the four digits is

• A. $240$
• B. $244$
• C. $586$
• D. $781$

Answer 1

The correct option is A $240$

$\to$ Four case: $(1,2,3,4,1)......(1,2,3,4)$

For $(1,2,3,4,1)=\frac{\angle 5}{\angle 2}$ ways $\left(2\right(1\left)\right)$

$=\frac{120}{2}=60$

Similarly for all $4$ cases $60$ ways $\Rightarrow 60\times 4=240$ total $\Rightarrow \left(A\right)$