How many three-digit odd integers less than 500 are there so that all the digits are not distinct?
A. 56
B. 88
C. 144
D. 200
E. 250
A. 56
B. 88
C. 144
D. 200
E. 250
While attacking counting problem always satisfy the restrictions first, so that you can freely select the rest. Here the restrictions are,psm12se wrote:How many three-digit odd integers less than 500 are there so that all the digits are not distinct?
- 1. Integers must be less than 500 ---> First digit can be either 1, 2, 3, or 4.
2. Integers must be odd ---> Last digit can be either 1, 3, 5, 7, or 9.
If we can calculate the number of three-digit odd integers less than 500 with all the digits different and subtract that from 200, we will have our answer.
Number of three-digit odd integers less than 500 with all the digits different...
- Numbers starting with 1 ---> (4 choice for last digit)*(8 choice for middle digit) --> 32
Numbers starting with 2 ---> (5 choice for last digit)*(8 choice for middle digit) = 40
Numbers starting with 3 ---> Same as numbers starting with 1 --> 32
Numbers starting with 4 ---> Same as numbers starting with 2 --> 40
The correct answer is A.
