Binomial Theorem And Its Simple Applications Question 45
Question: The value of $ {{(}^{7}}C_0+{{,}^{7}}C_1)+{{(}^{7}}C_1+{{,}^{7}}C_2)+…+ $ $ {{(}^{7}}C_6+{{,}^{7}}C_7) $ is
Options:
A) $ 2^{8}-2 $
B) $ 2^{8}-1 $
C) $ 2^{8}+1 $
D) $ 2^{8} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ {{(}^{7}}C_0+{{,}^{7}}C_1)+{{(}^{7}}C_1+{{,}^{7}}C_2)+….+{{(}^{7}}C_6+{{,}^{7}}C_7) $
$ ={{,}^{8}}C_1+{{,}^{8}}C_2+….+{{,}^{8}}C_7={{,}^{8}}C_0+{{,}^{8}}C_1+{{,}^{8}}C_2+… $
$ +{{,}^{8}}C_7+{{,}^{8}}C_8-({{,}^{8}}C_0+{{,}^{8}}C_8)=2^{8}-1(1+1)=2^{8}-2. $
BETA
