SOLUTION: Please help me solve this equation for a binomial expansion: Find the 5th term in the expansion of (2a - b)^9 Here is the work that I have done: n = 9 k = 4 n-k = 5

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Please help me solve this equation for a binomial expansion: Find the 5th term in the expansion of (2a - b)^9 Here is the work that I have done: n = 9 k = 4 n-k = 5       Log On

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Question 604308: Please help me solve this equation for a binomial expansion:
Find the 5th term in the expansion of (2a - b)^9
Here is the work that I have done:
n = 9 k = 4
n-k = 5 x = 2a
y = -b
(9 over 4)(2a)^5 (-b)4
The answer comes out as:
(126)(32a^5)(b^4)
How did they get 126 out of this problem?
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
It turns out that the "(9 over 4)" refers to the combination 9 C 4, which is

9 C 4 = (9!)/(4!(9-4)!) = (9*8*7*6*5!)/(4!5!) = (9*8*7*6)/(4*3*2*1) = 3024/24 = 126

So 9 C 4 = 126

They just used different notation to represent the same idea. Let me know if this makes sense.