The expression \(^nC_1\) represents a combination, specifically the number of ways to choose 1 item from a set of \(n\) distinct items. The formula for combinations is given by:

\[
^nC_r = \frac{n!}{r!(n-r)!}
\]

For \(^nC_1\):

\[
^nC_1 = \frac{n!}{1!(n-1)!}
\]

Since \(1!\) is 1 and \((n-1)!\) cancels out with part of \(n!\), we have:

\[
^nC_1 = \frac{n \times (n-1)!}{1 \times (n-1)!} = n
\]

So, \(^nC_1 = n\).

This means there are \(n\) ways to choose 1 item from a set of \(n\) items.

Would you like more details on combinations or how they are used in different scenarios? 

Here are 5 related questions:
1. What is the formula for \(^nC_r\) and how is it derived?
2. How do combinations differ from permutations?
3. How would you calculate \(^nC_2\) for a specific value of \(n\)?
4. Can you explain the real-world application of combinations in probability?
5. What happens to \(^nC_r\) when \(r = n\)?

**Tip:** Remember that combinations count selections where the order doesn't matter, unlike permutations, where order is important.

Explore ^nC1, the combination formula for choosing 1 item from a set of n items. Learn the formula nCr = n! / (r!(n-r)!) and its application. Suitable for high school students and those interested in probability and combinatorics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation