Aₐᵇ = a! / (a - b)!
Cₐᵇ = a! /b! (a - b)!
C₇³ = 7! / 3!(7 - 3)! = 7! / 3!*4!
C₇⁵ = 7! / 5!*(7 - 5)! = 7! / 5!*2!
A₁₀⁷ = 10! / (10 - 7)! = 10! / 3!
1 / A₁₀⁷ = 3! / 10!
C₇³ + C₇⁵ = 7! / 3!*4! + 7! / 5!*2! = 7!*(5/3!*5! + 3/3!*5! ) = 8!/3!*5!
6! (C₇³ + C₇⁵ ) / A₁₀⁷ = 6! 8! /3!5! * 3!/10! = 6!/5! * 8!/10! = 6 / 9*10 = 1/15
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Verified answer
Aₐᵇ = a! / (a - b)!
Cₐᵇ = a! /b! (a - b)!
C₇³ = 7! / 3!(7 - 3)! = 7! / 3!*4!
C₇⁵ = 7! / 5!*(7 - 5)! = 7! / 5!*2!
A₁₀⁷ = 10! / (10 - 7)! = 10! / 3!
1 / A₁₀⁷ = 3! / 10!
C₇³ + C₇⁵ = 7! / 3!*4! + 7! / 5!*2! = 7!*(5/3!*5! + 3/3!*5! ) = 8!/3!*5!
6! (C₇³ + C₇⁵ ) / A₁₀⁷ = 6! 8! /3!5! * 3!/10! = 6!/5! * 8!/10! = 6 / 9*10 = 1/15