⁹C₄ — Combination Value and Formula

⁹C₄ = 126. This is calculated using the combinations formula: ⁿCᵣ = n! / (r! × (n−r)!)

Question (Click to Flip)

What is ⁹P₄ (permutation)?

Answer

⁹P₄ = 9!/(9-4)! = 9!/5! = 9×8×7×6 = 3,024. This is 4! times ⁹C₄: 24 × 126 = 3024 ✓

Card 1 of 1 free previews

Key Facts

Pascal's Triangle contains all combination values! The rth element in the nth row of Pascal's Triangle equals ⁿCᵣ. The sum of the nth row = 2ⁿ (total subsets).

Formula and Calculation

Combinations Formula: ⁿCᵣ = n! / [r! × (n−r)!]

For ⁹C₄:

n = 9, r = 4
⁹C₄ = 9! / (4! × 5!)
= (9 × 8 × 7 × 6) / (4 × 3 × 2 × 1)
= 3024 / 24
= 126

Step-by-Step

Numerator: 9 × 8 × 7 × 6 = 3024 Denominator: 4! = 4 × 3 × 2 × 1 = 24

3024 ÷ 24 = 126

⁹C₄ = 126

Verification using symmetry: ⁹C₄ = ⁹C₅ (since 9−4=5) ⁹C₅ = 9!/(5!×4!) = same calculation = 126 ✓

What Does ⁹C₄ Mean?

⁹C₄ represents the number of ways to choose 4 items from 9 distinct items where order does NOT matter.

Example: From a class of 9 students, how many ways can you select a committee of 4? Answer: ⁹C₄ = 126 ways

Key difference:

Combination (ⁿCᵣ): Order doesn't matter — {A,B,C,D} = {D,C,B,A}
Permutation (ⁿPᵣ): Order matters — {A,B,C,D} ≠ {D,C,B,A}

Questions and Answers

What is ⁹P₄ (permutation)?+

⁹P₄ = 9!/(9-4)! = 9!/5! = 9×8×7×6 = **3,024**. This is 4! times ⁹C₄: 24 × 126 = 3024 ✓

More in Maths

📐

Latus Rectum of a Parabola — Formula and Length

Learn the latus rectum of a parabola. The latus rectum is the chord passing through the focus perpendicular to the axis. Length = 4a for parabola y² = 4ax.

📐

LCM का फुल फॉर्म क्या है? (LCM Full Form in Maths)

जानें गणित में LCM का फुल फॉर्म (Lowest Common Multiple) क्या होता है। लघुत्तम समापवर्त्य का भारी अर्थ और इसे निकालने का आसान तरीका।

📐

LCM of 10 and 15 (With Solution)

Find the LCM of 10 and 15 using prime factorization and listing multiples method. LCM = 30. Detailed step-by-step solution.

📐

What is the LCM of 12 and 18?

Learn how to find the exact LCM of 12 and 18 using the Prime Factorization method. Step-by-step math tutorial with clear examples.

📐

Find the LCM of 306 and 657 & The Largest 5 Digit Number

Learn how to calculate the LCM of 306 and 657 using prime factorization. Also, find out what the largest 5-digit number is.

Study Smarter with Shinyu.ai

Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.