interceptor77 wrote:
C(m,n) = (m!)/((m-n)!n!) for nonnegatives integers m and n, m>=n. If C(5,3)=C(5,x) and x≠3, what is the value of x?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5
The given expression should remind you that it is mCn i.e. selecting n out of total m items.
We know that mCn = mC(m-n) and hence 5C3 = 5C(5-3) = 5C2
Even if this doesn't strike you during the exam, simply substitute.
(m!)/((m-n)!n!) = 5!/3!*2! = 5!/(5-x)!*x!
(5-x)!*x! = 3!*2!
We see that x = 2
Answer (C)
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Karishma
Veritas Prep GMAT Instructor
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