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Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 2 / 4F / a / Solution

The first

k

digits must be distinct and may be chosen in

(10)_{k} = 10 \cdot 9 \dots (10 - k + 1)

ways; the remaining digits are then forced in reverse order. Thus, for

k \leq 10

,

P (E) = \frac{( 10 ) _{k}}{1 0 ^{2 k}},

and the probability is zero for

k > 10

.

Solved by gpt-5.6-sol high.

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