Math Problem Statement

What is the value of the binomial coefficient (3 choose 2)?

Solution

The expression in the image appears to be a binomial coefficient, which is typically written as (ab)\binom{a}{b}, denoting "a choose b." In this case, it looks like:

(32)\binom{3}{2}

This is interpreted as the number of ways to choose 2 elements from a set of 3, which is calculated using the combination formula:

(nk)=n!k!(nk)!\binom{n}{k} = \frac{n!}{k!(n-k)!}

So, for (32)\binom{3}{2}:

(32)=3!2!(32)!=3×2×12×1×1=62=3\binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3 \times 2 \times 1}{2 \times 1 \times 1} = \frac{6}{2} = 3

Thus, (32)=3\binom{3}{2} = 3.

Would you like more details on this topic or any additional clarifications?

Here are five related questions:

  1. How does the combination formula differ from the permutation formula?
  2. What is the value of (53)\binom{5}{3}?
  3. How do you calculate factorial values like 6!6! or 7!7!?
  4. What is the difference between combinations and arrangements?
  5. How would you use combinations to solve a probability problem?

Tip: In combinatorics, order does not matter for combinations, but it does for permutations.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Binomial Coefficient

Formulas

nCr = n! / (r! * (n - r)!)

Theorems

Combination Formula

Suitable Grade Level

Grades 8-10