Step One Develop Pascal's Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 <<<< How the 5th power expands.
Step Two Confirm that nCr gives the same thing as the triangle gives.
The third term is outlined as 10 a^3 b^2 The powers must add to 5. The 10 can be found this way
nCr Where n is the row number and r is the term you want so n = 5 r = 3 nCr = n! / [(n - r)! r!] 5C3 = 5! / ((3!) (2!) ) 5C3 = 5 * 4 / 2 5C3 = 10 Just as the triangle predicted.
