How many even numbers greater than 300 can be formed with digits 1,2,3,4,5 no digit being repeated ?	Choose the correct answer
A) 111 B) 123 C) 124 D) 132 E) 145
Number can be 3, 4, or 5 digit (4 and 5 digit number will obviously be more than 300).   5 digit even numbers:   Last digit must be either 2 or 4 (for number to be even), so 2 choices. First 4 digits can be arranged in 4! # of ways. So total # of 5 digit even numbers possible is 4!∗2=484!∗2=48;   4 digit even numbers:   Last digit again must be either 2 or 4, so 2 choices. # of ways to choose rest 3 digits out of 4 digits left when order of the digits matters is P34P43. So total # of 4 digit even numbers possible is P34∗2=48P43∗2=48;   3 digit even numbers:   Last digit again must be either 2 or 4, so 2 choices. # of ways to choose rest 2 digits out of 4 digits left when order of the digits matters is P24P42. So total # of 3 digit even numbers possible is P24∗2=24P42∗2=24.   But out of these 24 3-digit even numbers some will be less than 300, the ones starting with 1 or 2. There are 9 such numbers (1X2 and 3 options for the second digit X, so 3 plus 1X4 and 3 options for X, so 3 plus 2X4 and 3 options for X, so 3), which means that # of 3 digit even numbers more than 300 is 24−9=1524−9=15;   So total 48+48+15=11148+48+15=111.   111NS:111
<result>A</result>
How many even numbers greater than 300 can be formed with digits 1,2,3,4,5 no digit being repeated ?