Question

How many four digit numbers are there with distinct digits?

• A. $5040$
• B. $4536$
• C. $30240$
• D. $5274$

Answer 1

Answer: (B)

$\overline{\begin{array}{rl}& 9digits\\ & (1to9)\end{array}}$
$\overline{\begin{array}{rl}& 9digits\\ & (0to9)\end{array}}$
$\overline{\begin{array}{rl}& 8digits\\ & (0to9)\end{array}}$
$\overline{\begin{array}{rl}& 7digits\\ & (0to9)\end{array}}$
Except those digit used in first place
Except those digits used in Ist and IInd place
Except those digits used in Ist, IInd and IIIrd place
$\therefore$ Required number of digits $=9\times 9\times 8\times 7$ $=4536.$