Question

how many 4 digit numbers are there with no digit repeated​

Answer 1

Answer:

There are 10 differentdigits (0 to 9) with which four vacant places { }{ }{ }{ } are to

be filled up, repetition of digits not allowed. As the required numbers are of 4-digits, the first

place (thousand's place) has to be non-zero so there are 9 choices. So the first place can be filled

up in 9 ways. Having filled up the first place, the second place (hundred's place) can be filled

up in 9 ways by any of the remaining 9 digits as the repetition of digits is not allowed.Similarly, the third place (ten's place) can be filled up in 8 ways and the fourth place (unit'splace) can be filled up in 7 ways.By fundamental principle of counting, the required number of 4-digit numbers= 9 x9 x8x7 = 4536.