Question

How many 4 digit number are there with no digit repeated

Answer 1

Answer:

1023 us the correct answer

Answer 2

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Given , Repetition is not allowed

According to the question ,

Available digits are :

0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9

$</p><p>\large \fbox{} \: \fbox{} \: \fbox{} \: \fbox{}</p><p>$

$\star$ The first place can be filled in 9 different ways by anyone of the 1 to 9 digits

$\star$The second place can be filled in 9 different ways by anyone of the 0 to 9 remaining digits

$\star$The third place can be filled in 8 different ways by anyone of the remaining digits

$\star$The fourth place can be filled in 7 different ways by anyone of the remaining digits

Therefore ,

$\sf \to Total \: no. \: of \: ways \: = 9 × 9 × 8 × 7 \\ \\ \sf \to</p><p>Total \: no. \: of \: ways = 4536$

$\therefore$The required number is 4536