For row n = 5 in Pascal's triangle, the sum of the coefficients is 32. Which option shows that sum?

For row n = 5 in Pascal's triangle, the sum of the coefficients is 32. Which option shows that sum?

• A. 32
• B. 16
• C. 10
• D. 64

Answer: (A)

The sum of the numbers in a row of Pascal's triangle equals 2^n, where n is the row number, because that row comes from expanding (1 + x)^n and setting x to 1 sums all the coefficients. For row n = 5, the sum is 2^5, which is 32. In that row the coefficients are 1, 5, 10, 10, 5, 1, which add up to 32. So the option that shows 32 is the correct one.

The sum of the numbers in a row of Pascal's triangle equals 2^n, where n is the row number, because that row comes from expanding (1 + x)^n and setting x to 1 sums all the coefficients. For row n = 5, the sum is 2^5, which is 32. In that row the coefficients are 1, 5, 10, 10, 5, 1, which add up to 32. So the option that shows 32 is the correct one.