A-Math More P & C Qn! On forming numbers

How many even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated?

Conditions
#1: Even
#2: 5-digit number
#3: no digit is to be repeated

Case 1:When the first digit is odd (must be more than or equal to 5)

2C1 * 5P3 * 3C1

Logic & Reasoning:

first digit: either 5 or 7 so 2C1
last digit: either 2,4 or 6 so 3C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3

Case 2:When the first digit is even

5P3 * 2C1

Logic & Reasoning:

first digit: 6 so no need to choose just put!
last digit: either 2 or 4 so 2C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3

Total even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated = Case 1 + Case 2 = 480

:)