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Mathematics

What numbers are in the 5th row of Pascal's Triangle?

Answer

1 4 6 4 1

Explanation

Start with 1 at the top; each row begins and ends with 1, and each interior number is the sum of the two directly above it. Building row by row: 1; 1 1; 1 2 1; 1 3 3 1; 1 4 6 4 1. So the 5th row is 1 4 6 4 1. Pascal’s Triangle lists binomial coefficients: the k-th row (top counted as 1st) gives the coefficients of (a+b)^(k−1). For k=5, (a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4. You can also compute the entries as combinations: C(4,0), C(4,1), C(4,2), C(4,3), C(4,4). Memory tip: think “add the two above” and “perfect symmetry,” and remember the row’s numbers sum to 2^4 = 16.

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