Discrete mathematics
Counting without listing: the sum and product rules, permutations and combinations, with and without repetition. Discrete mathematics is tested in the Mathematics section of the Bocconi Test, which has 24 of the 50 questions (75 minutes in total, 2027/28 format). This guide covers it in 6 lessons, each with the rule that solves it and a diagram.
The sum and product rules
Choices made one after another multiply; separate alternatives add. Fill the most restricted place first, and count “at least one” as all minus none.
Permutations
n different objects can be ordered in n! ways; k ordered places from n objects give n!/(n − k)!. Objects that must stay together are glued into one block; “not together” is all minus together.
Permutations with repetition
k places each filled from n symbols, repeats allowed: nᵏ. Arranging n objects with groups of equal ones: n! divided by the factorial of each group. Shortest grid routes are words of R and U.
Combinations
Choosing k of n without order: C(n, k) = n!/(k!(n − k)!), the ordered count divided by k!. C(n, k) = C(n, n − k). Choices from separate groups multiply.
Combinations with repetition
k identical items into n boxes: a row of k balls and n − 1 bars, so C(n + k − 1, k) ways. Hand out the minimums first; subtract the cases that break a maximum.
Which formula?
Ask two questions: does order matter, and can an item be chosen again? The answers give nᵏ, n!/(n − k)!, C(n + k − 1, k) or C(n, k). Split mixed problems into stages and use the complement for “at least”.
What is the Bocconi Test format?
Online Bocconi Test for admission in academic year 2027/28, as published by Università Bocconi.
- Questions / time
- 50 / 75 minutes
- Distribution
- 24 mathematics · 11 reading · 6 numerical reasoning · 9 critical thinking
- Scoring
- +1 correct · 0 blank · −0.2 wrong
- Question languages
- English · Italian
- Three-option questions
- Some critical thinking questions have three options; a wrong answer there costs −0.33
- Minimum score
- Below 17 points the test is not considered for selection
- AI degree
- Mathematical and Computing Sciences for Artificial Intelligence also needs at least 11 of 24 points in mathematics
- Law test
- A separate test, 50 questions / 75 minutes: 5 mathematics · 11 reading · 6 numerical reasoning · 18 logic and critical thinking · 10 verbal reasoning; same scoring
Source: Università Bocconi, Online Bocconi Test page (checked October 7, 2026)
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