4p2+4C2−4p34p_2 + 4C_2 - 4p_34p2+4C2−4p3
npr=n!(n−r)! and nCr=n!(n−r)! r!np_r = \frac{n!}{(n-r)!} \text{ and } nC_r = \frac{n!}{(n-r)!\,r!}npr=(n−r)!n! and nCr=(n−r)!r!n!
= 4!(4−2)!+4!(4−2)! 2!−4!(4−3)!=4!2!+4!2! 2!−4!1!\frac{4!}{(4-2)!} + \frac{4!}{(4-2)!\,2!} - \frac{4!}{(4-3)!} = \frac{4!}{2!} + \frac{4!}{2!\,2!} - \frac{4!}{1!}(4−2)!4!+(4−2)!2!4!−(4−3)!4!=2!4!+2!2!4!−1!4!
= 4∗3∗2!2!+4∗3∗2!2! 2!−4∗3∗2∗11!\frac{4*3*2!}{2!} + \frac{4*3*2!}{2!\,2!} - \frac{4*3*2*1}{1!}2!4∗3∗2!+2!2!4∗3∗2!−1!4∗3∗2∗1
12 + 6 - 24 = -6
