How do use the binomial theorem to calculate 6C4?

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Answer 1 · 2017-04-17T17:02:36

$15$ $15$

$^{n} C_{r} = \frac{n!}{(n - r)! r!}$ $"^n C_r = (n!)/((n-r)! r!)$

$^{6} C_{4} = \frac{6!}{(6 - 4)! \cdot 4!} = \frac{6!}{2! \cdot 4!}$ $"^6 C _4 = (6!)/((6-4)! * 4!) = (6!)/(2! * 4!)$

$=( 6*5*cancel4*cancel3*cancel2*cancel1)/(( 2 * 1)*(cancel4*cancel3*cancel2*1) * )$

$= (6 * 5)/(2 * 1) = 15$

Answer 2 · 2017-12-09T03:36:56

This question requires a basic understanding of how to manipulate factorials.

Answer:

$""^6C_4=15$

Please refer to my video below for a fully worked explanation :)