The number of ways of dividing 15 men and 15 women into 15 couples, each consisting of a man and women, is

Number of ways of selecting 15 teams out of 15 women such that each term consists of a man and a woman

${=}^{15}{{\mathrm{C}}_1}^{15}{\mathrm{C}}_1{+}^{14}{{\mathrm{C}}_1}^{14}{\mathrm{C}}_1{+}^{13}{{\mathrm{C}}_1}^{13}{\mathrm{C}}_1+\dots ..{+}^1{{\mathrm{C}}_1}^1{\mathrm{C}}_1$

$={15}^2+{14}^2+{13}^2+\dots \dots .+1^2=\frac{15\times 16\times 31}{6}=1240$