[ \binom{7}{2} \times 2! = \frac{7!}{2!(7-2)!} \times 2 = \frac{7 \times 6}{2 \times 1} \times 2 = 21 \times 2 = 42 ]

Let's break down your equation step by step:

1. **Binomial Coefficient Definition**:
   \[
   \binom{7}{2} = \frac{7!}{2!(7-2)!}
   \]
   This is the formula for combinations. For \( \binom{7}{2} \), we have:
   \[
   \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21
   \]

2. **

\binom{7}{2} \times 2! = \frac{7!}{2!(7-2)!} \times 2 = \frac{7 \times 6}{2 \times 1} \times 2 = 21 \times 2 = 42

Explore how to calculate the combination \binom{7}{2} using factorials and multiplication. This detailed solution walks through the steps involved, covering key concepts in combinatorics and permutations. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation