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Probability Level 4

Which of the following must be equal to ∑ r = 0 2 n ( − 1 ) r ( 2 n r ) 2 \displaystyle\sum_{r = 0}^{2n}(-1)^r\dbinom{2n}{r}^2 ?

Notation : ( M N ) \dbinom MN denotes the binomial coefficient , ( M N ) = M ! N ! ( M − N ) ! \binom MN = \dfrac{M!}{N!(M-N)!} .

None of these choices ( 4 n 2 n ) \binom{4n}{2n} ( − 1 ) n ( 4 n 2 n ) (-1)^n\binom{4n}{2n} ( 2 n n ) \binom{2n}{n} ( − 1 ) n ( 2 n n ) (-1)^n\binom{2n}{n}

Sabhrant Sachan by Sabhrant Sachan , 21, India

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