Question 1024628: How many 4 digit numbers can be formed with
the 10 digit ie (.0,1,2,3,4,5,6,7,8,9) if
(a) repetitions are allowed.
(b) repetitions are not allowed.
(c) last digit must be zero and repetition are not allowed.
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! 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
|
|
|
