Answer:
The given statement is false.
Step-by-step explanation:
Given : The coefficient of [tex]x^k y^{n-k}[/tex] in the expansion of [tex](x+y)^n[/tex] equals [tex]\frac{n-k}{k}[/tex].
To find : True or False
Solution : The given statement is not true .
Because, when we do expansion of [tex](x+y)^n[/tex] by binomial theorem we get,
[tex](x+y)^n= ^{n}C_k x^k y^{n-k}[/tex]
Therefore, coefficient of [tex]x^k y^{n-k}[/tex] is [tex]^{n}C_k=\frac{n!}{(n-k)!k!}[/tex]
The given statement is false.
