Question

How many 4 digits number are there with no digit reputation?

Answer 1

4537 four

There are 4537 four digit-numbers with no digit repeated. Explanation : So we have 10 numbers, which are 0,1,2,3,4,5,6,7,8,9. And we have to make four digit numbers with no reputation.

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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

$\large \fbox{} \: \fbox{} \: \fbox{} \: \fbox{}$

$\star$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