Question 1158403: How many numbers of 5 digits can be made from the digits 1,2,3,4,5,6,7,8 and 9 when each number contains exactly one even digit and no digit is repeated?
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
ANSWER. (4*5)*(5*4*3*2) = 20*120 = 2400.
Explanation
(1) We can use any one of 4 even digits and can place it to any of 5 possible positions.
It gives the factor 4*5 = 20.
(2) Next we should place remaining 5 odd digits (1, 3, 5, 7 and 9) in remaining 4 positions.
(Notice that after placing the even digit in #(1), its position and remaining positions are just
determined by a unique way - they are not a subject of choice anymore).
Therefore, placing in #(2) can be done by 5*4*3*2 = 120 ways.
(3) In total, it gives 20*120 = 2400 different ways, in accordance with the answer above.
Solved.
|
|
|
