Evaluate `.^20C_5` + `sum_(r=2)^5`` .^(25-r)C_4`

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Evaluate : .^(20)C_(5)+sum_(j=2)^(5).^(25-j)C_(4)

sum_(r=2)^(n)(5r-3)C_(r)=

Evaluate the following: \ sum_(r=1)^5\ ^5C_r

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C(47,4)+sum_(r=1)^5 C(52-r,3)=

Prove that .^(35)C_(5) + sum_(r=0)^(4^((39-r))) C_(4) = .^(40)C_(5)

Prove that sum_(r=1)^5 ^5C_r=31