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TL;DR

The number of unordered subsets of r items from n distinct items: \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \), also called the binomial coefficient.

By Valenke Exam Prep Team·Last updated 2026-06-03

Combinations

The number of unordered subsets of r items from n distinct items: \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \), also called the binomial coefficient.

Why it matters for interviews

The binomial coefficient appears everywhere in quant interviews: probability distributions, counting arguments, combinatorial identities, and the binomial options pricing model.

Definition and Mathematical Foundation

The number of unordered subsets of r items from n distinct items: \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \), also called the binomial coefficient.

Application in Quantitative Finance

The binomial coefficient appears everywhere in quant interviews: probability distributions, counting arguments, combinatorial identities, and the binomial options pricing model.

Related Terms

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Frequently Asked Questions

What is Pascal's identity?▼
\( \binom{n}{r} = \binom{n-1}{r-1} + \binom{n-1}{r} \). This recursive formula generates Pascal's triangle and is the basis for dynamic programming solutions to combinatorial problems.
What is the Vandermonde identity?▼
\( \binom{m+n}{r} = \sum_{k=0}^{r} \binom{m}{k}\binom{n}{r-k} \). It counts choosing r items from two groups of sizes m and n. Useful in hypergeometric distribution derivations.
How do combinations relate to the binomial theorem?▼
\( (x+y)^n = \sum_{k=0}^n \binom{n}{k} x^k y^{n-k} \). The binomial coefficients are the expansion coefficients, connecting combinatorics to algebra and probability.