Question

50 POINTS PLEASE HELP ME!!!!!!!! HURRY!!!! 17. Evaluate 6! 8P5 12C4

Answer 1

Step-by-step explanation:

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