AMC 8 Daily Practice Round 9

Complete problem set with solutions and individual problem pages

Problem 5 Easy

Bill is choosing his courses for next year. He has to choosc two different courses, one from Foundational courses and one from Elective courses.

Foundational courses

Elective courses
Game AIGame AI
Database systemBiology
AlgebraItalian
GeometryHistory

How many different pairs of combinations are possible?

  • A.

    7

  • B.

    8

  • C.

    12

  • D.

    15

  • E.

    16

Answer:D

It is worth noting that Game AI courses are both in Foundational courses and in elective courses.

C_{3}^{1}\times C_{4}^{1}+1\times3=3\times4+3=15.

The answer is \text{D}.