Question

Suppose $5-$digit numbers are formed by the digits $1,2,3,4$ and $5$ without repetition . If they are arranged in an ascending order, then $100th$ number is

• A. $51243$
• B. $51423$
• C. $51234$
• D. $51342$

Answer 1

Answer: (D)

$51342$

Let

$1$ at ten thousand place

$\therefore$ Total numbers formed $=4!=24$

Similarly with ten-thousand be $2$

$\therefore$ Total numbers $=4!=24$

with $3$ at ten thousand place $\to 24$

and with $4$ at ten thousand place $\to 24$

$\therefore$ Total numbers $=24+24+24+24$

$=96$

$\therefore$ Now we have $5$ at ten-thousand place.

$\therefore 5\frac{1}{}\frac{2}{}\frac{3}{}\frac{4}{}\to {97}^{th}$

$51243\to {98}^{th}$

$51324\to {99}^{th}$

$51342\to {100}^{th}$

$51342$