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What is the value of 22C19?

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Math Revolution GMAT Instructor
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What is the value of 22C19?  [#permalink]

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New post 11 Sep 2018, 02:50
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

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[Math Revolution GMAT math practice question]

What is the value of 22C19?

\(A. 770\)
\(B. 1540\)
\(C. 3080\)
\(D. 4620\)
\(E. 6160\)

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Re: What is the value of 22C19?  [#permalink]

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New post 11 Sep 2018, 02:55
\(22C_{19}\) = \(\frac{22!}{19!3!}\) = \(\frac{22*21*20}{6}\) = 77*20 = 1540.

B is the answer.
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Re: What is the value of 22C19?  [#permalink]

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New post 11 Sep 2018, 05:58
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the value of 22C19?

\(A. 770\)
\(B. 1540\)
\(C. 3080\)
\(D. 4620\)
\(E. 6160\)


nCr = nCn-r

Thus:
22C19 = 22C22-19 = 22C3 = \(\frac{22*21*20}{3*2*1}\) = 22*7*10 = 1540


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Re: What is the value of 22C19?  [#permalink]

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New post 13 Sep 2018, 01:36
=>

Since \(nCn-r = nCr,\)
22C19 = 22C3 = \(\frac{(22*21*20)}{(1*2*3)} = 11*7*20 = 1540.\)

Therefore, the answer is B.
Answer: B
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Re: What is the value of 22C19?   [#permalink] 13 Sep 2018, 01:36
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