Question

50 POINTS PLEASE HELP ME!!!!!!!! HURRY!!!!

17. Evaluate

6!

8P5

12C4

Answer 1

Explanation:

`n!=\underbrace{1\cdot2\cdot3\cdot...\cdot n}\\\\6!=1\cdot2\cdot3\cdot4\cdot5\cdot6=720\\=======================\\_nP_r=(n!)/((n-r)!)\\\\_8P_5=(8!)/((8-5)!)=(8!)/(3!)=(3!\cdot4\cdot5\cdot6\cdot7\cdot8)/(3!)=4\cdot5\cdot6\cdot7\cdot8=6,720\\=======================\\_nC_r=(n!)/(r!(n-r)!)\\\\_(12)C_4=(12!)/(4!(12-4)!)=(4!\cdot5\cdot6\cdot...\cdot12)/(4!\cdot8!)=(5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12)/(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8)=495`