There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B.

Question

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is \_\_\_\_\_\_\_\_.

Answer: 5626

Accepted Answer

Group A
 Group B
 Ways

$4m$

$3m+1w$

$2m+2w$

$1m+3w$

$4w$

$1m+3w$

$2m+2w$

$3m+w$

$4m$

${}^{4}{C}_{4}\cdot {}^{4}{C}_{4}\, =1$

${}^{4}{C}_{1}\cdot {}^{5}{C}_{1}\cdot {}^{5}{C}_{4}^{1}{C}_{3}\, =400$

${}^{4}{C}_{2}\cdot {}^{5}{C}_{2}{}^{5}{C}_{2}{}^{4}{C}_{2}\, =3600$

${}^{4}{C}_{1}{}^{5}{C}_{3}{}^{5}{C}_{3}{}^{4}{C}_{1}\, =1600$

${}^{5}{C}_{4}{}^{5}{C}_{4}\, =25$

$\begin{gathered} =1+400+3600+1600+25 \ =5626 \end{gathered}$

Solutions · 1