Binomial Sum Powers (Jee Mains)

Terms of Binomial Expansion

Medium

Binomial Sum Powers

If ${1^2}.\left( {^{15}{C_1}} \right) + {2^2}.\left( {^{15}{C_2}} \right) + {3^2}.\left( {^{15}{C_3}} \right) + .... + {15^2}.\left( {^{15}{C_{15}}} \right)$ = 2^m·3ⁿ·5^k, where m, n, k ∈ N, then m + n + k is equal to :-

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