Subsets

How many 19 element's subsets can be made from the 26 element set?

Result

x =  657800

Solution:

C19(26)=(2619)=26!19!(26−19)!=26⋅25⋅24⋅23⋅22⋅21⋅207⋅6⋅5⋅4⋅3⋅2⋅1=657800  x=(2619)=657800C_{{ 19}}(26) = \dbinom{ 26}{ 19} = \dfrac{ 26! }{ 19!(26-19)!} = \dfrac{ 26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 } { 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } = 657800 \ \\ \ \\ x = { { 26 } \choose 19 } = 657800

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