Question

Va rog care ma puteți ajuta și pe mine repede

Answer 1

 

$\displaystyle\bf\\1a)\\C_7^3-C_5^2+C_{2021}^{2021}=\\\\=\frac{A_7^3}{P_3}-\frac{A_5^2}{P_2}+1=\\\\=\frac{7\times6\times5}{1\times2\times3}-\frac{5\times4}{1\times2}+1=\\\\=7\times5-5\times2+1=\\\\=35-10+1=25+1=\boxed{\bf26}\\\\\\1b)\\\Big(P_4+A_3^2\Big)(P_3-A_4^2)=\\\\=\Big(1\times2\times3\times4+3\times2\Big)\Big(1\times2\times3-4\times3\Big)=\\\\=\Big(24+6\Big)\Big(6-12\Big)=\\\\=30\times\Big(-6\Big)=\boxed{\bf-180}$

.

$\displaystyle\bf\\1c)\\23\%~din~\frac{15}{7}=\\\\=23\%\times\frac{15}{7}=\\\\=\frac{23}{100}\times\frac{15}{7}=\\\\=\frac{23\times15}{100\times7}=\frac{345}{700}=\boxed{\bf\frac{69}{140}}$