Question 957593: A four digit number greater than 5000 and divisible by 5 is to be formed using the digits 0,1,3,5,7 find the number of ways to do it (1) by repeating (2) without repeating
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
A four digit number greater than 5000 and divisible by 5 is to be formed using the digits 0,1,3,5,7 find the number of ways to do it
(1) by allowing repetition of digits
We can choose the first digit as 5 or 7. That's 2 ways.
We can choose the second digit as 0,1,3,5, or 7. That's 5 ways.
We can choose the third digit as 0,1,3,5, or 7. That's 5 ways.
We can choose the fourth digit as 0 or 5. That's 2 ways.
The answer would be 2×5×5×2 = 100. However since the problem states
"greater than 5000", we cannot include the number 5000. So we subtract
1 from 100.
Answer: 99 ways
---------------------------
(2) without repeating
When we cannot repeat, we must be careful to
1. consider the most restrictive choices first.
2. if one restrictive choice changes the restrictions on another choice,
the problem must be broken down into separate cases.
We have two restrictive digits to choose, the first and last. If we choose
5 for the first digit, that reduces the choices for the last digit.
Therefore we must consider two cases. Case 1 is when 5 comes first.
Case 2 is when 7 comes first.
Case 1: 5 comes first
We choose the first digit 1 way, as 5.
We choose the fourth digit 1 way, as 0.
We choose the second digit 3 ways, 1, 3, or 7
We choose the third digit any of the 2 remaining digits.
That's 1×1×3×2 = 6 ways.
Case 2: 7 comes first.
We choose the first digit 1 way, as 7.
We choose the fourth digit 2 ways, as 0 or 5.
We choose the second digit any of the 3 remaining digits.
We choose the third digit and of the 2 remaining digits.
That's 1×2×3×2 = 12 ways.
Total: 6+12 = 18 ways.
Edwin
|
|
|
