Math Problem Statement

${n \choose i+1}$

Solution

The binomial coefficient (ni+1)\binom{n}{i+1} is commonly expressed as:

(ni+1)=n!(i+1)!(n−(i+1))!=n!(i+1)!(n−i−1)!\binom{n}{i+1} = \frac{n!}{(i+1)!(n-(i+1))!} = \frac{n!}{(i+1)!(n-i-1)!}

where:

  • n!n! is the factorial of nn,
  • (i+1)!(i+1)! is the factorial of i+1i+1,

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Binomial Coefficients
Factorials

Formulas

Binomial coefficient: \binom{n}{i+1} = \frac{n!}{(i+1)!(n-i-1)!}
Factorial formula: n! = n × (n-1) × ... × 1

Theorems

Binomial Theorem

Suitable Grade Level

Grades 10-12

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