### Instruction: What is the 39th number in the row of Pascal's triangle that has 41 numbers?### Response: I know that Pascal's triangle is formed by adding the two numbers above each entry, starting from 1 on the sides.
The row with 41 numbers is the 40th row, since the first row is the 0th row.
I also know that the entries in each row are symmetrical, so the 39th number is the same as the 3rd number.
To find the 3rd number, I can use the formula for the binomial coefficients: (n choose k) = n! / (k! (n-k)!), where n is the row and k is the position from the left, starting from 0.
In this case, n = 40 and k = 2, so I get: (40 choose 2) = 40! / (2! 38!) = (40 * 39 * 38!) / (2 * 38!) = 20 * 39 = 780.