Binomial Theorem
Sum of alternating products of binomial coefficients
MMTS_Full_Test_19
Grade 12
Question:
If $\binom{30}{0}\binom{30}{20}-\binom{30}{1}\binom{30}{19}+\binom{30}{2}\binom{30}{18}-\cdots+\binom{30}{20}\binom{30}{0}={}^nC_r$, then maximum possible value of $n+r$ equals
Step-by-Step Solution
Key Concept: The sum $=$ coeff of $x^{20}$ in $(1-x)^{30}(1+x)^{30}=(1-x^2)^{30}=$ coeff of $x^{20}$ in $(1-x^2)^{30}=\binom{30}{10}$.
Maximum $n+r=30+20=50$.
Correct Answer: 50