Question

explicatia pas cu pas,va rog și dau coronă​

Answer 1

Trebuie sa cunosti bine formulele pentru combinari si aranjamente.

C₆³ = 6! / 3!(6-3)! = 3!×4×5×6 / 3!×3! = 4×5×6 / 1×2×3 = 120 / 6 = 20

A₄² = 4! / (4-2)! = 2!×3×4 / 2! = 12

Asadar: 20 - 12 + 3 = 10

Answer 2

$\displaystyle C_6^3-A_4^2+3 \\\\ \boxed{C_n^k=\frac{n!}{k!(n-k)!} }~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\boxed{A_n^k=\frac{n!}{(n-k)!} }\\\\\\ C_6^3=\frac{6!}{3!(6-3)!} =\frac{6!}{3! \cdot 3!} =\frac{\not3! \cdot 4 \cdot 5 \cdot 6}{\not3! \cdot 1 \cdot 2 \cdot 3} =\frac{120}{6} =20\\\\\\ A_4^2=\frac{4!}{(4-2)!} =\frac{4!}{2!} =\frac{\not2! \cdot 3 \cdot 4}{\not2!} =12\\\\\\ C_6^3-A_4^2+3=20-12+3=\underline{\underline{11}}$