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# A company has enough money to buy five different colour

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GMAT Instructor
Joined: 04 Jul 2006
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A company has enough money to buy five different colour [#permalink]  09 Jul 2006, 03:35
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A company has enough money to buy five different colour printers for its ten sales offices. If each sales office has room for as many as three printers, in how many ways can the printers be allocated?

(A) 90540 (B) 90940 (C) 99540 (D) 99640
(E) none of these
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Joined: 02 Mar 2006
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Total number of ways irrespective of room for printers = 10 ^ 5
= 100000

Now, the restriction is atmost we can arrange 3 printers per office

we will subtract the possibility of arranging 5 or 4 printers per office to get the desired result

for 5 printers = 5C5 * 10C1 = 10 ---------- (1)

for 4 printers = (5C4 * 10C1) * (1C1 * 9C1) = 450 ---------- (2)

adding (1) & (2) = 460

when we subtract above from 100000 gives 99540

Is this Correct????????
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