I am to evaluate the following:
C(7,2)
answer:21
C(12,7)
answer: 66
This is the one I can't figure out
the coefficient of x7y2 in the expansion of (2x-y)9
any help is appreciated
Hello, papa_chango123!
Evaluate: .$\displaystyle C(7,2)$
. . Answer: 21 . . . Right!
$\displaystyle C(12,7)$
. . Answer: 66 . . . no
$\displaystyle C(12,7) \:=\:\frac{12!}{7!5!} \:=\:\frac{12\cdot11\cdot10\cdot9\cdot8}{5\cdot4\c dot3\cdot2\cdot1} \:=\:792$
Find the coefficient of $\displaystyle x^7y^2$ in the expansion of $\displaystyle (2x-y)^9$
You're expected to know the Binomial Expansion.
The term with $\displaystyle x^7y^2$ is: .$\displaystyle C(9,7)(2x)^7(-y)^2$
Hence, we have: .$\displaystyle \frac{9!}{7!2!}(2^7x^7)(y^2)\;=\;\boxed{4608}x^7y^ 2$