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$\text{We can Do this Question using Logic or by using Properties of Multinomial Thm } \\ \text{1st Method : logic } \\ \text{We can see that each term is Basically getting multiplied by 26 letters } \\ \text{ so Total Terms = } 26\times26=676 \\ \text{But only terms like }a^2,b^2..z^2 \text{ are Unique, Terms like } ab,ba \text{ and } za ,az\text{ will merge } \\ \text{Subtracting the unique 26 terms from total terms , we need to divide the rest by 2} \\ \text{We get : Terms = }\dfrac{676-26}{2}=325 \\ \text{Now add the unique terms Back in terms , we get our Total Terms : }\boxed{325+26 = 351}$

$\text{2nd Method : Multinomial } \\ \text {From a Property of Binomial Thm.} \\ \text{Coefficient of a term in } (a+b+c+d+...)^n \text { is :} \\ \dfrac{n!}{{n_1!}\times{n_2!}\times{n_3!}\times{n_4!}\times{....}}\times{a^{n_1}}\times{b^{n_2}}\times{c^{n_3}}\times{d^{n_4}\times{....}} \\ \text{Where } n_1+n_2+n_3+n_4+\cdots=n \text{ and } 0\le{n_1,n_2,n_3,n_4,...}\le{n}\\ \text{In this case } n_1+n_2+n_3+\cdots+n_{26}=2 \\ \text{Total Number of terms = Number of Integral Solutions of this equation }\\ \implies \binom{2+26-1}{26-1} \implies \binom{27}{25}\\ \implies \text{Ans : }\boxed{\dfrac{27\times{26}}{2}=351}$