Question

Binomial Distribution, anyone? :)

Answer 1

Use the Binomial Theorem to find the binomial expansion of the expression.
\[(d - 5)^{6}\]

Answer 2

Are you familiar with C(n,r) ?

Answer 3

I got the answer choices here..

A) \[d ^{6} + 6d ^{5} + 15d ^{4} + 20d ^{3} + 15d ^{2} + 6d + 1\]

B) \[d ^{6} + 30d ^{5} + 375d ^{4} + 2500d ^{3} + 9375d ^{2} + 18750d + + 15625\]

C) \[d ^{6} - 30d ^{5} + 375d ^{4} - 2500d ^{3} + 9375d ^{2} - 18750d + 15625\]

Answer 4

\[(a+b)^n\ = \sum \left(\begin{matrix}n \\ i\end{matrix}\right) a^i \ b^{n-i}\]

Answer 5

The first term is d^6.
If you expand it, the second term is na^(n-1)b
which in the given case,
n=6.
a=d
b=-5
so the second term is 6d^5 (-5) = -30d^5
That good enough to make a choice?

Answer 6

Answer C!! :)

Answer 7

oooh makes sense that the + and - are alternating since the equation at the beginning has a minus sign...

Answer 8

thank you for your explanation!

Answer 9

Right, and the choice is correct!

Answer 10

So if my equation is \[(d + 3)^{7} \] it has all + and no -. And the second term is also na^(n-1)b?

Answer 11

Yep, would you like to give it a try?

Answer 12

the second term is \[7d^{6}\] ?

Answer 13

Almost, you just missed out the last bit!

Answer 14

I missed the times 3...

Answer 15

21d^6 it is! Good job!

Answer 16

so it's \[21d ^{6}\] ?

Answer 17

yees thank you!! :)

Answer 18

No problem.
If you like to try the third term, you're welcome to do so.

Answer 19

i got it all right thanks to you! thank you so much. best response given :)

Answer 20

You're welcome! :)