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If 10!/(10-r)!<1,000, what is the greatest possible value of r?

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If 10!/(10-r)!<1,000, what is the greatest possible value of r?  [#permalink]

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New post 10 Jul 2017, 01:02
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If \(\frac{10!}{(10-r)!}<1,000\), what is the greatest possible value of r?

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

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If 10!/(10-r)!<1,000, what is the greatest possible value of r?  [#permalink]

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New post 10 Jul 2017, 07:43
1
MathRevolution wrote:
If \(\frac{10!}{(10-r)!}<1,000\), what is the greatest possible value of r?

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


\(\frac{10!}{(10-r)!}<1,000\)

By Checking the options the Greatest possible value of \(r\) is \(= 5\)

Lets check the value of \(r = 5\)

\(\frac{10!}{(10-5)!}\) \(=> \frac{10!}{5!}\)

\(\frac{10*9*8*7*6 * 5!}{5!}\) \(=> 10*9*8*7*6\)

\((10*9 = 90)\) and \((8*7 = 56)\) ------------ (i)

\(90*50 = 4500\) ------- (This value is greater than \(1000\))

Therefore (i) will have value greater than \(1000\).

Hence \(5\) cannot be the value of \(r\).

If we have the value without \(7\) in (i), we will get a value less than \(1000\).

Lets check for value of \(r = 3\)

\(\frac{10!}{(10-3)!}\) \(=> \frac{10!}{7!}\)

\(\frac{10*9*8*7!}{7!}\)

\(10*9*8 = 720\) ------------- (Less than \(1000\))

Therefore greatest possible value of \(r = 3\)

Answer (C)...


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Re: If 10!/(10-r)!<1,000, what is the greatest possible value of r?  [#permalink]

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New post 12 Jul 2017, 01:10
==>If you substitute r=1, 2, 3, 4.., for r=4, you get 10!/(10-4)!=10*9*8*7=5,040>1,000, and for r=3, you get 10!/(10-3)!=10*9*8=720<1,00.

Thus, the greatest possible value of r is r=3. The answer is C.
Answer: C
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Re: If 10!/(10-r)!<1,000, what is the greatest possible value of r?   [#permalink] 12 Jul 2017, 01:10
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