SOLUTION: Five digit numbers of different digits are formed at random from the digits { 0, 1, 2, 3, 4, 5, 6 }. What is the probability that number formed is even?

Algebra ->  Permutations -> SOLUTION: Five digit numbers of different digits are formed at random from the digits { 0, 1, 2, 3, 4, 5, 6 }. What is the probability that number formed is even?      Log On


   

Question 946470: Five digit numbers of different digits are formed at random from the digits { 0, 1, 2, 3, 4, 5, 6 }. What is the probability that number formed is even?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
0, 1, 2, 3, 4, 5, 6
Case 1: When the first digit is 2, 4 or 6.

Choose the 1st digit 3 ways.  (2, 4 or 6) 
Choose the 5th digit 3 ways.  (use 0 or the 2 even digits still unused) 
Choose the 2nd digit 7 ways.
Choose the 3rd digit 6 ways.
Choose the 4th digit 5 ways. 

That's 3x3x7x6x5 = 1890

Case 2: When the first digit is 1, 3 or 5.

Choose the 1st digit 3 ways.  (1, 3 or 5) 
Choose the 5th digit 4 ways.  (0, 2, 4, or 6) 
Choose the 2nd digit 7 ways.
Choose the 3rd digit 6 ways.
Choose the 4th digit 5 ways.

That's 3x4x7x6x5 = 2520

Total: 1890+2520 = 4410.

Edwin