How do you find the binomial coefficient of 8C6?

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Answer 1 · 2017-03-11T16:15:06

$""^8C_6 = 28$

We want to calculate:

$( (8), (6) ) = ""^8C_6$

We can either use a calculator, if you have that functionality. It is often labelled $""^nC_r$

$""^8C_6 = 28$

On advanced TI calculators (eg TI-nspire), you use the $ncr$ function:

$ncr(8,6) = 28$

Otherwise we calculate using the definition:

$""^nC_r = (n!)/(r!(n-r)!)$

Which gives us:

$""^8C_6 = (8!)/(6!(8-6)!)$
$" "= (8!)/(6!2!)$
$" "= (1*2*3*4*5*6*7*8)/((1*2*3*4*5*6)(1*2))$
$" "= (7*8)/(2)$
$" "= 7*4$
$" "= 28$