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.Com
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(20054)   (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
RELATED QUESTIONS

digits:1,2,3,4,5,6,7,8,9 No repetition is allowed a)how many 5 digit numbers are there... (answered by Edwin McCravy,AnlytcPhil)
1. How many different 4-digit numbers can be formed from the digits 2, 3, 4, 5, 6, 7, and (answered by Alan3354)
A student was asked to form two-digit numbers using the following digits:... (answered by ikleyn)
I saw this solution online from a tutor (ikelyn). I think there's a mistake in it and i... (answered by math_tutor2020,ikleyn)
How many two-digit even numbers can you form using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8,... (answered by Edwin McCravy,ikleyn)
How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if... (answered by MathLover1)
Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to determine how many three digit numbers (answered by ikleyn)
Four-Digit Number. How many four-digit numbers can be formed using the digits 0, 1, 2, 3, (answered by MathLover1,jilalbenkad)
How many two-digit even numbers can you form using the digits 0, 1 , 2, 3, 4, 5, 6, 7, 8, (answered by greenestamps)