What is ${}^{n}C_{r}$ in probability?

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Solution

Interpretation of ${}^{n}C_{r}$ .
In probability, ${}^{n}C_{r}$ is the number of ways of selection of $r$ elements from a set of $n$ elements, such that the order of elements does not matter.
Formula: ${}^{n}C_{r} = \frac{n!}{r! (n - r)!}$

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Similar questions

^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r}

Write the expression $^{n} C_{r + 1} +^{n} C_{r - 1} + 2 \times^{n} C_{r}$ in the simplest form.

^{n} C_{r} + {4.}^{n} C_{r - 1} + {6.}^{n} C_{r - 2} + {4.}^{n} C_{r - 3} +^{n} C_{r - 4} =

^{n} C_{r - 1} = 36,^{n} C_{r} = 84

^{n} C_{r + 1} = 126

r

\sum_{r = 0}^{n - 1} \frac{n_{C_{r}}}{n_{C_{r}} + n_{C r + 1}}

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