ID012 · Algebraic identities · Classes 8–12
Pascal triangle
Pascal's triangle starts with 1; each number is the sum of the two numbers above it. Row n gives the coefficients of (a + b)ⁿ, and its numbers add to 2ⁿ.
1 5 10 10 5 1Pascal triangle
📐 Formula
C(n, k) = C(n − 1, k − 1) + C(n − 1, k)
✏️ Worked example
Row 5: 1, 5, 10, 10, 5, 1, which adds to 32 = 2⁵.
🌍 Where it is used
Counting paths, choices and probabilities.
❓ Quick check
What is the sum of row 4?
🏋️ Practice
EasyWrite row 3.
Answer: 1 3 3 1
MediumWrite row 6.
Answer: 1 6 15 20 15 6 1
ChallengeWhich number appears in every row?
Answer: 1