How many 4-digit nunbers are there with no digit repeated?

Explanation

There are total 10 digits from 0 to 9.
`:'` The numbers cannot starts from 0.
So, numbers of ways of filling first place = 9
Number of ways of filling second place = 9
Number of ways of filling third place = 8
Number of ways of filling four place = 7
Total 4 digit numbers `= 9 xx 9 xx 8 xx 7 = 4536`.
Alternate Method:
There are 10 digits from 0 to 9.
Total 4 digit numbers taking from 10 digits `=.^(10)P_(4)` But in these numbers, those numbers are also included which start from 0, such numbers will be of 3 digits.
Numbers starting from `0 = .^(9)P_(3)`
Therefore, 4 digit numbers in which 0 is not at thousand's place `= .^(1)P_(4) - .^(9)P_(3)`
`= (10!)/(6!) - (9!)/(6!)`
`= (10 xx 9 xx 8 xx 7 xx 6!)/(6!) - (9 xx 8 xx 7 xx 6!)/(6!)`
`= 5040 - 504 - 4536`.