Verified answer

Необходимые формулы :

[tex]P_{n}=n!\ ,\ \ A_{n}^{k}=n\cdot (n-1)\cdot ...\cdot (n-k+1)\ ,\ C_{n}^{k}=\dfrac{A_{n}^{k}}{n!}\\\\\\5P_3-C_{10}^4+3A_5^2=5\cdot 3!-\dfrac{10\cdot 9\cdot 8\cdot 7}{4!}+3\cdot 5\cdot 4=5\cdot 6-10\cdot 3\cdot 7+60=\\\\=30-210+60=-120[/tex]

[tex]\displaystyle\bf\\P_{3} =3!=1\cdot 2\cdot 3=6\\\\\\C_{10} ^{4} =\frac{10!}{4!\cdot(10-4)!} =\frac{6!\cdot 7\cdot 8\cdot9\cdot 10}{1\cdot 2\cdot 3\cdot 4\cdot 6!} =7\cdot 3\cdot 10=210\\\\\\A_{5} ^{2} =\frac{5!}{(5-2)!} =\frac{3!\cdot 4\cdot 5}{3!} =4\cdot 5=20\\\\\\5P_{3}-C_{10} ^{4} +3A_{5} ^{2} =5\cdot6-210+3\cdot 20=30-210+60=-120\\\\\\Otvet: \ -120[/tex]