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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