A) \[^{60}{{C}_{20}}\]
B) \[^{30}{{C}_{10}}\]
C) \[^{60}{{C}_{30}}\]
D) \[^{40}{{C}_{30}}\]
Correct Answer: B
Solution :
\[{{(1-x)}^{30}}={{\,}^{30}}{{C}_{0}}{{x}^{0}}-{{\,}^{30}}{{C}_{1}}{{x}^{1}}+{{\,}^{30}}{{C}_{2}}{{x}^{2}}\]\[+......+{{(-1)}^{30}}{{\ }^{30}}{{C}_{30}}{{x}^{30}}\] ....(i) \[{{(x+1)}^{30}}={{\,}^{30}}{{C}_{0}}{{x}^{30}}+{{\,}^{30}}{{C}_{1}}{{x}^{29}}+{{\,}^{30}}{{C}_{2}}{{x}^{28}}\]\[+......+{{\,}^{30}}{{C}_{10}}{{x}^{20}}+....+{{\,}^{30}}{{C}_{30}}{{x}^{0}}\] ....(ii) Multiplying (i) and (ii) and equating the coefficient of x20 on both sides, we get required sum = coefficient of x20 in (1 - x2)30=30C10.
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