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\(^nC_r=\frac{n!}{r!(n-r)!}\\ so\\ ^8C_5=\frac{8!}{5!*3!}\\ ^8C_5=\frac{6*7*8}{1*2*3}\\ ^8C_5=\frac{7*8}{1}\\ ^8C_5=56\)​

8C5 = 8!/((8-5)!*5!) → 8!/(3!*5!) →  8*7*6*5!/(3!*5!) → 8*7*6/(3!) → 8*7*6/6 → 8*7 → 56

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what's 8C5? amd how to do it without using a calculator?

\(\begin{array}{rcll} && ^8C_5 \\\\ &=&\dbinom{8}{5} \\\\ &=&\dbinom{8}{8-5} \\\\ &=&\dbinom{8}{3}\\\\ &=&\dfrac{8}{3}\cdot \dfrac{7}{2} \cdot \dfrac{6}{1}\\\\ &=&\dfrac{8}{2}\cdot \dfrac{7}{1} \cdot \dfrac{6}{3}\\\\ &=&4\cdot 7 \cdot 2\\\\ &=& 56 \end{array} \)