What is the value of 10 C 2

1 answer:

6 0

The formula to use is the nCr combination formula
n C r = (n!)/(r!*(n-r)!)
where the exclamation marks indicate factorial notation

Plug n = 10 and r = 2 into the formula
n C r = (n!)/(r!*(n-r)!)
10 C 2 = (10!)/(2!*(10-2)!)
10 C 2 = (10!)/(2!*8!)
10 C 2 = (10*9*8!)/(2!*8!)
10 C 2 = (10*9)/(2!)
10 C 2 = (10*9)/(2*1)
10 C 2 = 90/2
10 C 2 = 45

Answer: 45

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$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{5})~\hspace{10em} \stackrel{slope}{m}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}(x-\stackrel{x_1}{2}) \\\\\\ y-5=-x+2\implies y=-x+7$