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# Rank these three quantities from least to greatest.

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Rank these three quantities from least to greatest.  [#permalink]

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23 Oct 2018, 03:02
00:00

Difficulty:

75% (hard)

Question Stats:

41% (01:35) correct 59% (01:48) wrong based on 86 sessions

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Ⅰ. $$\frac{49!}{(7^{49})^2}$$

Ⅱ. $$\frac{49!}{(7!)^2}$$

Ⅲ. $$\frac{49!}{(42!)(7!)}$$

Rank these three quantities from least to greatest.

A. I, II, III
B. I, III, II
C. II, I, III
D. II, III, I
E. III, I, II

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Re: Rank these three quantities from least to greatest.  [#permalink]

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23 Oct 2018, 03:37
Bunuel wrote:
Ⅰ. $$\frac{49!}{(7^{49})^2}$$

Ⅱ. $$\frac{49!}{(7!)^2}$$

Ⅲ. $$\frac{49!}{(42!)(7!)}$$

Rank these three quantities from least to greatest.

A. I, II, III
B. I, III, II
C. II, I, III
D. II, III, I
E. III, I, II

Ⅰ. $$\frac{49!}{(7^{49})^2}$$ Since Denominator is too big so this will be in decimals and a very small number in comparison to others

Ⅱ. $$\frac{49!}{(7!)^2} = 7*8*47*23*3*11*43*42!/7!$$

Ⅲ. $$\frac{49!}{(42!)(7!)} = \frac{49*48*47*46*45*44*43*42!}{42!7!}= 7*8*47*23*3*11*43$$

I is least and II is largest

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Re: Rank these three quantities from least to greatest.   [#permalink] 23 Oct 2018, 03:37
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