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 so5C1*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

:)

## 2 comments:

woah alot of math.. interesting blog.. feel free to visit mine at www.yanpingluvhim.blogspot.com

hey. i just want to clarify something that i'm not very sure of.

is

nCr x r! = nPr??thanks. (:

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