Let Us Count It On!
1. a. There are four choices for the hundreds digit (excluding zero), four choices for the tens digit (including zero), and only three choices for the units digit. By the Fundamental Principle of Counting, the total number of three-digit numbers under the given condition is
(4)(4)(3)=48
b.1. In this situation, a number is even if it ends in 0,4, or 6. The number of three digit numbers ending in either 4 or 6 is
(3)(3)(2)=18
And the number of three-digit numbers ending in 0 is
(4)(3)(1)=12
Hence, there are 18+12=30 even numbers.
b.2 a number is odd if it ends in 5 or 9. There are
(3)(3)(2)=18
b.3 A number is greater than 600 if the hundreds digit is 6 or 9. Thus,
(2)(4)(3)= 24 of the numbers in (a) are greater than 600.
c. If repetition of digits is allowed, there would be
(4)(5)(5)=100 three-digit numbers
2. 7P5= 7!/2!= (7)(6)(5)(4)(3)=2,520
3. Twelve different numbers can be formed from the digits of the 5,696. They are
5,966 6,659 6,569
9,566 6,695 6,965
5,669 5,696 6,596
9,665 9,656 6,956
4. 10P3= 10!/7!= (10)(9)(8)=720.
(4)(4)(3)=48
b.1. In this situation, a number is even if it ends in 0,4, or 6. The number of three digit numbers ending in either 4 or 6 is
(3)(3)(2)=18
And the number of three-digit numbers ending in 0 is
(4)(3)(1)=12
Hence, there are 18+12=30 even numbers.
b.2 a number is odd if it ends in 5 or 9. There are
(3)(3)(2)=18
b.3 A number is greater than 600 if the hundreds digit is 6 or 9. Thus,
(2)(4)(3)= 24 of the numbers in (a) are greater than 600.
c. If repetition of digits is allowed, there would be
(4)(5)(5)=100 three-digit numbers
2. 7P5= 7!/2!= (7)(6)(5)(4)(3)=2,520
3. Twelve different numbers can be formed from the digits of the 5,696. They are
5,966 6,659 6,569
9,566 6,695 6,965
5,669 5,696 6,596
9,665 9,656 6,956
4. 10P3= 10!/7!= (10)(9)(8)=720.