Trinity

How many different triads can be selected from the group 43 students?

Correct result:

n =  12341

Solution:

n=C3(43)=(433)=43!3!(43−3)!=43⋅42⋅413⋅2⋅1=12341n = C_{{ 3}}(43) = \dbinom{ 43}{ 3} = \dfrac{ 43! }{ 3!(43-3)!} = \dfrac{ 43 \cdot 42 \cdot 41 } { 3 \cdot 2 \cdot 1 } = 12341

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