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Binomial

by mgmt_gmat » Fri Feb 12, 2010 2:04 am
C(m,n) = m! / [(m-n)! n!] for nonnegative 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
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by sanju09 » Fri Feb 12, 2010 2:15 am
mgmt_gmat wrote:C(m,n) = m! / [(m-n)! n!] for nonnegative 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
If C(m, n) = m! / [(m - n)! n!], then C(m, m - n) = m! / [(m - m + n)! (m - n)!] = m! / [(m - n)! n!] = C(m, n).

Hence, C(m, n) = C(m, m - n) or C(5, 3) = C(5, 5 - 3) = C(5, 2) = C(5, x) [given] or x = [spoiler]2[/spoiler].

[spoiler]C[/spoiler]
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by ajith » Fri Feb 12, 2010 11:43 am
mgmt_gmat wrote:C(m,n) = m! / [(m-n)! n!] for nonnegative 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
C(5,3) = 5!/2!*3!
C(5,x) = 5!/ x! (5-x)!

2!*3! = x!*(5-x)!

either x =2 or x =3

since x=2 is not possible x =3
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