How do use the binomial theorem to calculate 10C7?

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How do use the binomial theorem to calculate 10C7?

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Answer 1 · 2017-08-15T09:41:36

$120$ $120$

Explanation:

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

$x^{n} C_{r} = \frac{n!}{r! (n - r)!}$ $color(white)(x)^nC_r=(n!)/(r!(n-r)!)$

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

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

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

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

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How do use the binomial theorem to calculate 10C7?

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