SOLUTION: digits:1,2,3,4,5,6,7,8,9 a)how many 5 digit numbers are there that exclude 0 and 7 b) How many of them start with an even number c) how many of them start and end with and even

Algebra ->  Permutations -> SOLUTION: digits:1,2,3,4,5,6,7,8,9 a)how many 5 digit numbers are there that exclude 0 and 7 b) How many of them start with an even number c) how many of them start and end with and even       Log On


   

Question 843930: digits:1,2,3,4,5,6,7,8,9
a)how many 5 digit numbers are there that exclude 0 and 7
b) How many of them start with an even number
c) how many of them start and end with and even number

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
a)how many 5 digit numbers are there that exclude 0 and 7
The digits that exclude 0 and 7 are {1,2,3,4,5,6,8,9}

Choose the first digit 8 ways.
Choose the second digit 8 ways.
Choose the third digit 8 ways.
Choose the fourth digit 8 ways
Choose the fifth digit 8 ways.

8×8×8×8×8 = 85 = 32768 ways.
b) How many of them start with an even number
Choose the first digit 4 ways.
Choose the second digit 8 ways.
Choose the third digit 8 ways.
Choose the fourth digit 8 ways
Choose the fifth digit 8 ways.

4×8×8×8×8 = 4×84 = 4×4096 = 16384 ways.
c) how many of them start and end with and even number
Choose the first digit 4 ways.
Choose the second digit 8 ways.
Choose the third digit 8 ways.
Choose the fourth digit 8 ways
Choose the fifth digit 4 ways.

4×8×8×8×4 = 4×83×4 = 4×512×4 = 8192 ways.

Edwin