how many even numbers greater than 300 cab be formed with the digits 1,2,3,4,5, no repetitions being allowed
Dear student
If the number is > 300 if must have at least 3 digits
There are only 5 digits to choose so it must have either 3 4 or 5 digits.
3 digit numbers:
the first digit must be 3 4 or 5
If the first digit is 3 or 5 (2 choices) the last digit must be 2 or 4 (2 choices) and there are 3 choices for the middle digit
That makes 2x2x3 = 12 choices
If the first digit is 4, the last digit must be 2 and there are 3 choices for the middle digit.
So there are 15 3-digit numbers.
4 digit numbers:
the last digit must be 2 or 4 (2 choices)
The others can be anything so there are 2 x 4 x 3 x 2 = 48 choices
5 digit numbers:
Similar the 4 digit numbers
There are 2 x 4 x 3 x 2 x 1 = 48 choices
Total number = 48 + 48 + 15 = 111
Regards
If the number is > 300 if must have at least 3 digits
There are only 5 digits to choose so it must have either 3 4 or 5 digits.
3 digit numbers:
the first digit must be 3 4 or 5
If the first digit is 3 or 5 (2 choices) the last digit must be 2 or 4 (2 choices) and there are 3 choices for the middle digit
That makes 2x2x3 = 12 choices
If the first digit is 4, the last digit must be 2 and there are 3 choices for the middle digit.
So there are 15 3-digit numbers.
4 digit numbers:
the last digit must be 2 or 4 (2 choices)
The others can be anything so there are 2 x 4 x 3 x 2 = 48 choices
5 digit numbers:
Similar the 4 digit numbers
There are 2 x 4 x 3 x 2 x 1 = 48 choices
Total number = 48 + 48 + 15 = 111
Regards