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a70
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During a war a Major is supposed to send 5 units of soldiers to 5 diff 28 Sep 2018, 09:56
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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95% (hard)

Question Stats:

32% (02:13) correct 68% (02:03) wrong based on 148 sessions

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During a war a Major is supposed to send 5 units of soldiers to 5 different borders. If he has 30 soldiers and has to send an equal number of soldiers to 5 regions, in how many ways can he do so?

A. \(30!/(5!)^6\)

B. \(30!/(5!)^5\)

C. \(30!/(6!)^5\)

D. \((30!/6!^5)5!\)

E. \(30!/(6!^5*5!)\)
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C
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chetan2u
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GMAT Focus 1: 735 Q90 V89 DI81
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During a war a Major is supposed to send 5 units of soldiers to 5 diff 28 Sep 2018, 10:50
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a70
During a war a Major is supposed to send 5 units of soldiers to 5 different borders. If he has 30 soldiers and has to send an equal number of soldiers to 5 regions, in how many ways can he do so?

A. \(30!/(5!)^6\)

B. \(30!/(5!)^5\)

C. \(30!/(6!)^5\)

D. \((30!/6!^5)5!\)

E. \(30!/(6!^5*5!)\)
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Straight formula ..
If you have to make 5 groups of 6 people from (5*6) people, answer is \(\frac{(5*6)!}{(6!)^5}\)

Now if you do not know the formula..
First 6 can be selected in 30C6
Next 6 from remaining 24 in 24C6 and so on
So 30C6*24C6*18C6*12C6*6C6
\(\frac{30!}{24!6!}*\frac{24!}{18!6!}*\frac{18!}{12!6!}*\frac{12!}{6!6!}*\frac{6!}{0!6!}=\frac{30!}{6!6!6!6!6!}=\frac{30!}{(6!)^5}\)

C
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GyMrAT
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During a war a Major is supposed to send 5 units of soldiers to 5 diff 30 Sep 2018, 09:14
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a70
During a war a Major is supposed to send 5 units of soldiers to 5 different borders. If he has 30 soldiers and has to send an equal number of soldiers to 5 regions, in how many ways can he do so?

A. \(30!/(5!)^6\)

B. \(30!/(5!)^5\)

C. \(30!/(6!)^5\)

D. \((30!/6!^5)5!\)

E. \(30!/(6!^5*5!)\)
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Using the concept, if 2n different items are to divided into 2 groups of n items each, then it can be done in \(\frac{(2n)!}{{n!*n!*2!}}\)

Here we have 30 soldiers, hence 5*6 items to be divided into 5 groups of 6 items each.

30 soldiers can be divided into 5 units of 6 soldiers each in \(\frac{30!}{((6!)^{5}*5!)}\)

The 5 units can then be sent to the 5 different borders in 5! ways.

Hence total # of ways of doing this is = \(\frac{30!}{((6!)^{5}*5!)}*5!\) = \(30!/(6!)^5\)


Answer C.


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GyM
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During a war a Major is supposed to send 5 units of soldiers to 5 diff 30 Sep 2018, 09:42
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Quote:
During a war a Major is supposed to send 5 units of 6 soldiers in each unit to 5 different borders. Into how many groups the 30 soldiers may be divided?

A. \(30!/(5!)^6\)

B. \(30!/(5!)^5\)

C. \(30!/(6!)^5\)

D. \((30!/6!^5)5!\)

E. \(30!/(6!^5*5!)\)
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[In the original question stem, we could send (say) just 5 soldiers -one to each border - from the 30 soldiers available, without violating the restrictions imposed.]

\(?\,\,:\,\,\,\# \,\,{\rm{groups}}\)

Border A: C(30,6) choices
Border B: C(24,6) choices
Border C: C(18,6) choices
Border D: C(12, 6) choices
Border E: C(6,6) choices or, if you prefer, the soldiers left ("no choices" then).

Using the Multiplicative Principle, we have:

\(?\,\,\, = \,\,\,\left( {{{30!} \over {6!\,\,24!}}} \right)\,\,\left( {{{24!} \over {6!\,\,18!}}} \right)\left( {{{18!} \over {6!\,\,12!}}} \right)\,\,\left( {{{12!} \over {6!\,\,6!}}} \right)\,\,\, = \,\,\,{{30!} \over {{{\left( {6!} \right)}^5}}}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Deyoz
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During a war a Major is supposed to send 5 units of soldiers to 5 diff 01 Apr 2021, 14:27
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can some one please explain why it is not 30!*5! / 6!^5 , since first we have to select five groups of 6 armies, which is 30!/6!^5 and arranging this number group in five boarders will give (30!/6!^)* 5!.

please help me to understand, where i am wrong ???
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During a war a Major is supposed to send 5 units of soldiers to 5 diff 19 Feb 2025, 07:50
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The intended answer can only be supported by making an assumption not warranted by the question stem.

The question stem refers to an equal number of soldiers being sent to each area.

This language does not preclude sending 1,2,3,4,5 or 6 to each area.

So the correct answer is much greater than the provided answer.
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