SOLUTION: How many 7-digit numbers can you form using the digits 2, 3, 4, 6, 5, 1, 0 if the numbers formed are even numbers with non-repeating digits?

Algebra ->  Probability-and-statistics -> SOLUTION: How many 7-digit numbers can you form using the digits 2, 3, 4, 6, 5, 1, 0 if the numbers formed are even numbers with non-repeating digits?      Log On


   

Question 1118502: How many 7-digit numbers can you form using the digits 2, 3, 4, 6, 5, 1, 0 if the numbers formed are even numbers with non-repeating digits?
Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 7-digit number number be "ABCDEFG"

Case 1: G = 0

Choose ABCDEF any of 6! ways.

Answer for Case 1:  6! = 720

Case 2. G is not 0.

Choose the 7th digit G any of 3 ways 
     (as 2, 4 or 6)
Choose the 1st digit A any of 5 ways 
     (Any of the 5 unchosen digits other than 
      0 or the digit chosen for the 7th) 
Choose the middle 5 digits BCDEF in 5! = 120 ways

Answer for case 2: 3∙5∙5! = 1800

Final answer: 720+1800 = 2520 possible 7-digit even numbers.

Edwin