a test consists of 10 true or false questions followed by 10 multiple choice questions, each with 5 choices. How many ways can Faith mark her answer to this test?
To find the total number of ways Faith can mark her answers on the test, we need to calculate the number of combinations for each section of the test and then multiply them together.
For the true or false questions:
Since each question only has two options (true or false), Faith has 2 choices for each question. With 10 true or false questions, the number of ways she can mark her answers is 2^10 (2 raised to the power of 10).
For the multiple-choice questions:
Each multiple-choice question has 5 choices, so Faith has 5 options for each question. Since there are 10 multiple-choice questions, the number of ways she can mark her answers is 5^10 (5 raised to the power of 10).
To find the total number of ways Faith can mark her answers, we multiply the number of ways for the true or false questions by the number of ways for the multiple-choice questions:
Total ways = 2^10 * 5^10.
Now, let's calculate the total number of ways Faith can mark her answers to this test:
Total ways = 1024 * 9765625
Total ways = 10,000,000,000
Therefore, Faith can mark her answers to this test in 10 billion ways.