C(m,n) = m! / [(m-n)! n!] for nonnegative integers m and n, m >/ n (m greater then equals 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
A. 0
B. 1
C. 2
D. 4
E. 5
Hi gmater,gmater29 wrote:C(m,n) = m! / [(m-n)! n!] for nonnegative integers m and n, m >/ n (m greater then equals 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
I'm going to take "x! = 3" as "x does not equal 3" (because, if x is a "nonnegative integer," then it is impossible for x! to equal 3).
We see that this is the combinatorics formula. The equation in the question is telling us what 5C3 equals. C (m,n) and C (5,3) is telling you to sub in 5 for m and 3 for n. And if we use the formula, we find that 5C3 is 10.
The question wants us to figure out what 5CX is. Because 5C3 equals 5CX, and because 5C3 equals 10, we already know that 5CX equals 10.
This question forces us to refer to the answer choices, and the answer chocies are numbers. So we have to backsolve.
Looking at the choices, we can reason that the answer should be closer to 3, and start with either B, C or D.
plugging in, you will find that 5C2 is also 10.
Choose C
