Question

Evaluate combination and permutations 9C4 and 6P4

Answer 1

`\\\\nCk=C^k_n=\left(\begin{array}{cc}k\\n\end{array}\right)=(n!)/(k!(n-k)!)\\\\9C4=C^4_9=\left(\begin{array}{cc}9\\4\end{array}\right)=(9!)/(4!(9-4)!)=(9!)/(4!\cdot5!)=(5!\cdot6\cdot7\cdot8\cdot9)/(2\cdot3\cdot4\cdot5!)\\\\=7\cdot2\cdot9=126\\----------------------------------\\nPk=P^n_k=\left(\begin{array}{cc}n\\k\end{array}\right)=(n!)/((n-k)!)\\\\6P4=P^6_4=(6!)/((6-4)!)=(6!)/(2!)=(2!\cdot3\cdot4\cdot5\cdot6)/(2!)=3\cdot4\cdot5\cdot6=360`