Question

what about this one??
Use the binomial coefficient formula to calculate the binomial coefficient for the 8th term in a polynomial expansion when the power of the binomial is 10.

Answer 1

\[\left(\begin{matrix}10 \\ 8\end{matrix}\right) =\frac{8!}{8!(10-8)!} = 45\]

Answer 2

i dont get it the answer can not be 45

Answer 3

This is using the combination formula. The value 45 is the coefficient. Oh and I made a typo, the 8! in the numerator should be 10!

Answer 4

could you solve it with all the steps? please

Answer 5

\[\left(\begin{matrix}10 \\ 8\end{matrix}\right)=\frac{10!}{8!(10-8)!}\]


\[\left(\begin{matrix}10 \\ 8\end{matrix}\right)=\frac{10!}{8!2!}\]


\[\left(\begin{matrix}10 \\ 8\end{matrix}\right)=\frac{10*9*8!}{8!2!}\]


\[\left(\begin{matrix}10 \\ 8\end{matrix}\right)=\frac{10*9}{2!}\]


\[\left(\begin{matrix}10 \\ 8\end{matrix}\right)=\frac{10*9}{2*1}\]


\[\left(\begin{matrix}10 \\ 8\end{matrix}\right)=\frac{90}{2}\]


\[\left(\begin{matrix}10 \\ 8\end{matrix}\right)=45\]

Answer 6

720
22
120
240
those are the possibility

Answer 7

Oh I made the silly mistake in thinking that x=8 is the 8th term, it's actually x=7 (since x starts at 0)


So \[\left(\begin{matrix}10 \\ 7\end{matrix}\right)=\frac{10!}{7!(10-7)!}=120\]

Answer 8

ok could you solve this one with steps as well?

Answer 9

What is the fourth term for the geometric sequence whose first term is 3 and whose ratio is 2?

Answer 10

\[\left(\begin{matrix}10 \\ 7\end{matrix}\right)=\frac{10!}{7!(10-7)!}\]


\[\left(\begin{matrix}10 \\ 7\end{matrix}\right)=\frac{10!}{7!3!}\]


\[\left(\begin{matrix}10 \\ 7\end{matrix}\right)=\frac{10*9*8*7!}{7!3!}\]


\[\left(\begin{matrix}10 \\ 7\end{matrix}\right)=\frac{10*9*8}{3!}\]


\[\left(\begin{matrix}10 \\ 7\end{matrix}\right)=\frac{10*9*8}{3*2*1}\]


\[\left(\begin{matrix}10 \\ 7\end{matrix}\right)=\frac{720}{6}\]


\[\left(\begin{matrix}10 \\ 7\end{matrix}\right)=120\]

Answer 11

What is the fourth term for the geometric sequence whose first term is 3 and whose ratio is 2?