how many Even Numbers greater than 300 can be formed with the digits 1, 2, 3, 4, 5 which cannot be repeated
Answers
3-digit numbers: Must begin with 3, 4, 5, and must end with 2, or 4. So if the first digit is 3 or 5, the last digit can be 2 or 4, and the 2nd digit can be any of the 3 remaining digits: 2*2*3=12. If the first digit is 4, then the last digit has to be 2, and the 2nd can be any of the 3 remaining: 1*1*3=3. 12+3=15 total such 3-digit numbers.
4-digit numbers: The last digit has to be 2 or 4. Then the first digit can be any of the 4 remaining digits, the 2nd has 3 choices, and the 3rd has 2: 2*4*3*2=48 such numbers.
5-digit numbers: Again, the last digit has to be 2 or 4, then the first has 4 options, the 2nd has 3, the 3rd has 2 and the 4th has 1: 2*4*3*2*1=48 such numbers.
Numbers with more than 5 digits require replication, and those with less than 3 aren’t bigger than 300, so that’s all of the options. 48+48+15=111 total such numbers.