# Binomial theorum based Solved Anser Query.

1. Aug 30, 2015

### nilesh_pat

Dear Sir,

Please help me to guide. The question is , Determine the seventh term, t[7], in the expansion of (2x - 3)[11].
Ans is
The seventh term is generated by substituting r = 6 into the general term formula.
n = 11, a = 2x, b = -3, and r = 6,
t[r+1] = [n]c[r]a[n-r]b[r]

t[6+1] = [11]c[6]a[11-6]b[6]

Please guide how [11]c[6] = 462

t[7] = 462 (2x)[5]-3[6]

With Regards
Nilesh.

2. Aug 31, 2015

### SteamKing

Staff Emeritus
The notation 11C6 means the number of groups of 6 items taken from a total of 11 items. It's called a combination and it is calculated using the formula:

$_nC_k=\frac{n!}{k!(n-k)!}$

https://en.wikipedia.org/wiki/Combination

3. Aug 31, 2015

### nilesh_pat

Could you please solve this using your formula step by step. Actually how to write the steps .

With regards,

Nilesh.

4. Aug 31, 2015

### nilesh_pat

Once again thank you sir, It is fully explain at wiki. and I Solved it.

Thanks once's again.

With Regards
Nilesh.