Bridge cards

How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts?

Correct result:

n =  1244117160

Solution:

C4(13)=(134)=13!4!(13−4)!=13⋅12⋅11⋅104⋅3⋅2⋅1=715 C6(13)=(136)=13!6!(13−6)!=13⋅12⋅11⋅10⋅9⋅86⋅5⋅4⋅3⋅2⋅1=1716 C1(13)=(131)=13!1!(13−1)!=131=13 C2(13)=(132)=13!2!(13−2)!=13⋅122⋅1=78 s=4+6+1+2=13 n=(s4)⋅ (s6)⋅ (s1)⋅ (s2)=715⋅ 1716⋅ 13⋅ 78=1244117160=1.244117⋅109

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3{2*-2}-4{2*-1}<12

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