Answer to Question #263698 in Combinatorics | Number Theory for she

Question

 A code have 4 digits in a specific order, the digits are between 0-9. How many different permutations are there if one digit may only be used once?

Answer 1

Code is four digited and of specific order with the condition that digits 0 to 9 once used , will not be repeated.

To find the number of permutations let us create four blanks

$\frac{}{1st-blank}, \frac{}{2nd-blank}, \frac{}{3rd-blank}, \frac{}{4th-blank}$ First blank can be filled by any one digit of 0 to 9, that is by 10 ways . For each way of filling first blank, the second blank can be filled by 9 ways as repetition not allowed. So first two blanks can be filled by 10x9 ways. Proceeding this way all the blanks can be filled by 10x9x8x7 ways i.e. 5040 ways.

So there are 5040 different permutations .