How many 4 digit numbers can be formed with the
10 digits i.e., (.0,1,2,3,4,5,6,7,8,9) if
(a) repetitions are allowed.
You can do this two ways.
First way:
There are 9999 integers from 1 to 9999 inclusive.
There are 999 integers from 1 to 999 inclusive which
have fewer than 4 digits. So there are 9999-999 or
9000 4 digit-numbers.
Second way:
Choose the first digit 9 ways from {1,2,3,4,5,6,7,8,9}
the first digit cannot be 0.
Choose the second digit any of 10 ways {0,1,2,3,4,5,6,7,8,9}
Choose the third digit any of 10 ways {0,1,2,3,4,5,6,7,8,9}
Choose the fourth digit any of 10 ways {0,1,2,3,4,5,6,7,8,9}
That's 9*10*10*10 = 9000 4-digit numbers
(b) repetitions are not allowed.
Choose the first digit 9 ways from {1,2,3,4,5,6,7,8,9}
the first digit cannot be 0.
Choose the second digit any of 9 ways.
It can be 0.
Choose the third digit any of 8 ways.
Choose the fourth digit any of 7 ways.
That's 9*9*8*7 = 4536 ways.
(c) last digit must be zero and repetition are not allowed.
Choose the last digit 1 way.
Choose the first digit any of 9 ways.
Choose the second digit any of 8 ways.
Choose the third digit any of 7 ways.
That's 1*9*8*7 = 504 ways.
Edwin