Pattern ${\mu }_{1111}^{abcd}$ ${\mu }_{1112}^{abcd}$ [4] ${\mu }_{1122}^{abcd}$ [3] ${\mu }_{1123}^{abcd}$ [6] ${\mu }_{1234}^{abcd}$ $abcd$ $\frac{{n}_{a}}{n}$ $\frac{4{n}_{a}\left({n}_{a}-1\right)}{n\left(n-1\right)}$ $\frac{3{n}_{a}\left({n}_{a}-1\right)}{n\left(n-1\right)}$ $\frac{6{n}_{a}\left({n}_{a}-1\right)\left({n}_{a}-2\right)}{n\left(n-1\right)\left(n-2\right)}$ $\frac{{n}_{a}\left({n}_{a}-1\right)\left({n}_{a}-2\right)\left({n}_{a}-3\right)}{n\left(n-1\right)\left(n-2\right)\left(n-3\right)}$ $a|bcd$ 0 $\frac{{n}_{a}{n}_{b}}{n\left(n-1\right)}$ 0 $\frac{3{n}_{a}{n}_{b}\left({n}_{b}-1\right)}{n\left(n-1\right)\left(n-2\right)}$ $\frac{{n}_{a}{n}_{b}\left({n}_{b}-1\right)\left({n}_{b}-2\right)}{n\left(n-1\right)\left(n-2\right)\left(n-3\right)}$ $ab|cd$ 0 0 $\frac{{n}_{a}{n}_{b}}{n\left(n-1\right)}$ $\frac{{n}_{a}{n}_{b}\left({n}_{a}+{n}_{b}-2\right)}{n\left(n-1\right)\left(n-2\right)}$ $\frac{{n}_{a}\left({n}_{a}-1\right){n}_{b}\left({n}_{b}-1\right)}{n\left(n-1\right)\left(n-2\right)\left(n-3\right)}$ $a|b|cd$ 0 0 0 $\frac{{n}_{a}{n}_{b}{n}_{c}}{n\left(n-1\right)\left(n-2\right)}$ $\frac{{n}_{a}{n}_{b}{n}_{c}\left({n}_{c}-1\right)}{n\left(n-1\right)\left(n-2\right)\left(n-3\right)}$ $a|b|c|d$ 0 0 0 0 $\frac{{n}_{a}{n}_{b}{n}_{c}{n}_{d}}{n\left(n-1\right)\left(n-2\right)\left(n-3\right)}$