Properties of binomial coefficient:

For the sake of expediency the coefficients ⁿC₀ , ⁿC₁ , . . ., ⁿC_r , . . .  ,ⁿC_n are generally denoted by C₀, C₁ ,  . . . , C_r , . . .  ,C_n respectively

• C₀ + C₁ + C₂ +. . . . . + C_n = 2ⁿ
• C₀ - C₁ + C₂ -. . . . . + (-1)ⁿ C_n = 0
• C₀ + C₂ + C₄ +. . . . . = C₁ + C₃ + C₅ +. . . . . = 2^n-1
• ⁿC_r1 + ⁿC_r2 => r₁ = r₂ or r₁ + r₂ = n
• ⁿC_r + ⁿC_r-1 = ⁿ⁺¹C_r
• r ⁿC_r =n ^n-1C_r-1
•  .

Problem: Calculate the value of

Solution: The provided value is 

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