Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Discrete mathematics, continuous mathematics and probability / 2 / b

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- Solution b

Solution

There are

n (n - 1) \dots (n - k + 1) = n! / (n - k)!

ordered selections of

k

distinct elements. Every size-

k

subset appears in exactly

k!

orders, giving the binomial coefficient

(k n) = \frac{n !}{k ! ( n - k )!}, 0 \leq k \leq n .

For

k = 0

, both the empty selection and

0!

contribute one.

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