How do use the binomial theorem to calculate 10C7?

1 Answer
Jim G.
Aug 15, 2017

#120#

Explanation:

#"using the definition of the "color(blue)"binomial coefficient"#

#color(white)(x)^nC_r=(n!)/(r!(n-r)!)#

#"where "n! =n(n-1)(n-2)......xx1#

#rArr^(10)C_7=(10!)/(7!xx3!)#

#color(white)(xxxxxx)=(10xx9xx8xxcolor(red)cancel(7xx6xx5xx4xx3xx2))/(color(red)cancel(7xx6xx5xx4xx3xx2)xx3xx2#

#color(white)(xxxxxx)=(10xx9xx8)/(3xx2)=120#

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