birthday←{⎕IO←0                     ⍝ probability of same birthday.
    ⍝ ⍺ : number of possible values
    ⍝ ⍵ : number of random values
    ⍝ p ← ⍺ birthday ⍵ : probability that there is one couple with same value
    ⍝ p ←→ 1-(!⍺)÷((⍺*⍵)×(!⍺-⍵))    ⍝ Birthday solution
    ⍝ (1-p) ←→ ((!⍺)÷(!⍺-⍵))÷(⍺*⍵)  ⍝ Rewrite of the equation
    ⍝ (1-p) ←→ (×/⍺-⍳⍵)÷(⍺*⍵)       ⍝ Definition of ! (⎕IO←0)
    ⍝ (1-p) ←→ ×/(⍺-⍳⍵)÷⍺           ⍝ Definition of *
    ⍝ (1-p) ←→ *+/(⍟⍺-⍳⍵)-⍟⍺        ⍝ Definition of ⍟
    11::1-*+/(⍟⍺-⍳⍵)-⍟⍺             ⍝ (×/) failed : take log
    11::1-×/(⍺-⍳⍵)÷⍺                ⍝ (!⍺) failed : try full computation
    1-((!⍺)÷(!⍺-⍵))÷(⍺*⍵)           ⍝ Try exact computation (faster)
}
code_colours

test script

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