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Probability + Power

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by harsh.champ » Fri Feb 05, 2010 10:27 pm
P is the number of ways of distributing 200 apples into five distinct boxes such that each box contains same number of apples. Find the highest power of 5 in P.


A. 5
B. 4
C. 3
D. 2
E. 1


The OA is E.
Seeking help regarding problem approach.
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by shashank.ism » Fri Feb 05, 2010 10:43 pm
P = 200!/((25!)^8)
The highest power of 5 in 200! = 40 +8+ 1 = 49
The highest power of 5 in 25! = 5 + 1 = 6.
The highest power of 5 in 25!^8 = 6 x 8 =48
Therefore, the highest power of 5 in P = 49 - 48 = 1
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by Maze » Sat Feb 06, 2010 12:33 am
shashank.ism wrote:P = 200!/((25!)^8)
The highest power of 5 in 200! = 40 +8+ 1 = 49
The highest power of 5 in 25! = 5 + 1 = 6.
The highest power of 5 in 25!^8 = 6 x 8 =48
Therefore, the highest power of 5 in P = 49 - 48 = 1


can you explain how u obtained the value of P??
Last edited by Maze on Sat Feb 06, 2010 12:59 am, edited 1 time in total.
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by Maze » Sat Feb 06, 2010 12:51 am
P = 200C40 * 160C40 * 120C40 * 80C40 * 40C40 = 200!/(40!)^5

Powers of 5 in 200! = 200/5 + 40/5 + 8/5(only take the quotient) = 49
Powers of 5 in 40! = 40/5 + 8/5 = 9
Powers of 5 in (40!)^5 = 9*5 = 45

Hence Maximum Power of 5 in P = 49-45 = 4
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