Let’s define f(x,y) as the probability of getting x of one suit and y of another. This function is not limited to two terms. With two arguments f(x,y)= combin(13,x)*combin(13,y)*12/combin(52,5). With three arguments f(x,y,z)= combin(13,x)*combin(13,y)*combin(13,z)*12/combin(52,5). With four arguments f(w,x,y,z)=combin(13,w)*combin(13,x)*combin(13,y)*combin(13,z)*4/combin(52,5). The probability of all four suits is COMBIN(13,1)3*COMBIN(13,2)*4/combin(52,5) = 26.37%. The probability of three suits is COMBIN(13,3)*COMBIN(13,1)2*12 + COMBIN(13,1)*COMBIN(13,2)^2*12/combin(52,5) = 58.84% The probability of two suits is COMBIN(13,3)*COMBIN(13,2)*12 + COMBIN(13,4)*COMBIN(13,1)*12/combin(52,5) = 14.59% The probability of one suit (including straight and royal flushes ) is 4*combin(13,5)/combin(52,5) = 0.20%. So three suits are the most frequent outcome.