52\ cards=26\ black\ cards\ +\ 26\ red\ cards\\ \\|\Omega|= \left ( {{52} \atop {5}} \right)= \frac{52!}{5!\cdot47!} = \frac{52\cdot51\cdot50\cdot49\cdot48\cdot47!}{2\cdot3\cdot4\cdot5!\cdot47!}= 13\cdot17\cdot25\cdot49\cdot48\\ \\1\ black\ card\ and\ the\ rest\ red\ cards\\ \\|A|=\left ( {{26} \atop {1}} \right)\cdot \left ( {{26} \atop {4}} \right)=26\cdot \frac{26!}{4!\cdot22!}= 26\cdot \frac{26\cdot25\cdot24\cdot23\cdot22!}{2\cdot3\cdot4\cdot22!}= 13\cdot13\cdot25\cdot4\cdot23\\ &amp;#10;