A test has 15 truefalse questions then a choice of either co

A test has 15 true-false questions, then a choice of either completing 5 multiple choice questions with 1 correct answer out of 4, or completing 4 multiple choice questions with correct answer out of 5. How many different completed answer sheets are there?

Solution

total sheets = 5 x ⁴C₁ x 2¹⁵ + 4 x ⁵C₁ x 2¹⁵ = 2 x 20 x 2¹⁵ = 5 x 2¹⁸