Solve the problem.
-On a History test, Keith Kepler must write an essay for 2 of the 7 questions in Part 1, and 4 of the 6 questions in Part 2. How many different combinations of questions can he answer?
A)36
B)10
C)315
D)15,120

Question

Quizplus · Accepted Answer

The number of ways Keith can choose 2 questions from Part 1 is 7 choose 2 or 21.
The number of ways Keith can choose 4 questions from Part 2 is 6 choose 4 or 15.
Using the multiplication principle, the total number of different combinations of questions Keith can answer is 21 x 15 = 315. Therefore, the best choice is C. The number of ways Keith can choose 2 questions from Part 1 is $\binom{7}{2}=21$. The number of ways he can choose 4 questions from Part 2 is $\binom{6}{4}=15$. To find the total number of combinations, we multiply these two outcomes: $21	imes 15 = 315$ combinations. Therefore, the answer is (C) 315.

Solve the Problem. -On a History Test, Keith Kepler Must Write an Essay