There are five different boxes with building materials. In how many ways those boxes could be distributed among six floores of a building if exactly one of the boxes should be on the fifth floor and the other four could be placed at any other floor.
I am also getting 600 as the answer.
Lets say we have five boxes A, B, C, D, E.
And 6 floors F1, F2, F3, F4, F5, F6
Either of 5 boxes can be kept on F5 floor hence 5 ways.
Let's keep F6 as empty 1st.
For each of the above 5 way, we have, 4 boxes placed in on floors F1, F2, F3 and F4 in 4! ways = 4.3.2 = 24.
Hence we have 24.5 = 120 ways of keeping boxes on 5 floors when F6 is empty.
Now we can repeat this exercise for each floor except F5. So we have 120 ways for each 5 floors which comes as 120 * 5 = 600 ways. I am sure we are not missing anything. Hence I think the answer is 600.
Vlad77, Could you please check if you have not done any typo ..
What is the OA ?