Concept explainers
a.
To find: How many three-digit numbers are possible under each condition.
a.

Answer to Problem 23E
Number of three-digit numbers formed under given condition
Explanation of Solution
Given information:
The leading digit cannot be Zero.
If there are no restrictions, there are 10 possibilities for each digit of a three-digit number.
As the leading digit cannot be zero so there are only 9 possibilities for first -digit of a three-digit number and there are 10 possibilities for remaining two digits of a three-digit number.
Therefore,
Number of three-digit numbers formed under given condition
b.
To find: How many three-digit numbers are possible under each condition.
b.

Answer to Problem 23E
Number of three-digit numbers formed under given condition
Explanation of Solution
Given information:
The leading digit cannot be Zero and no repetition is allowed.
If there are no restrictions, there are 10 possibilities for each digit of a three-digit number.
As the leading digit cannot be zero so there are only 9 possibilities for first -digit of a three-digit number and there are 9 possibilities for second digit of a three-digit number because as there no repetition is allowed as out of 10 possibilities one number is already used for first digit so there will be only 9 Possibilities for second digit of three-digit number.
There are 8 possibilities for third digit of a three-digit number because as there is no repetition is allowed as out of 10 possibilities one number is already used for first digit and another number is used for second digit so there will be only 8 Possibilities for third digit of three-digit number.
Therefore,
Number of three-digit numbers formed under given condition
c.
To find: How many three-digit numbers are possible under each condition.
c.

Answer to Problem 23E
Number of three-digit numbers formed under given condition
Explanation of Solution
Given information:
The leading digit cannot be Zero and number must be multiple of 5.
If there are no restrictions, there are 10 possibilities for each digit of a three-digit number.
As the leading digit cannot be zero so there are only 9 possibilities for first -digit of a three-digit number and there are 9 possibilities.
For a number to be Multiple of five, it’s last digit must be either 0 or 5.
So, number of possibilities for last digit of three-digit number is 2.
Number of Possibilities for second digit of a three-digit number is 10 as we can use any of the available possibilities.
Therefore,
Number of three-digit numbers formed under given condition
d.
To find: How many three-digit numbers are possible under each condition.
d.

Answer to Problem 23E
Number of three-digit numbers formed under given condition
Explanation of Solution
Given information:
The number is at least 400.
If there are no restrictions, there are 10 possibilities for each digit of a three-digit number.
If the number is at least 400, the first digit can only be
There are no restrictions for remaining digits.
So, number of possibilities for first digit are 6.
Number of Possibilities for second digit and third digit of a three-digit number is 10 as we can use any of the available possibilities.
Therefore,
Number of three-digit numbers formed under given condition
Chapter 9 Solutions
EBK PRECALCULUS W/LIMITS
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