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 #