Marking 15 true-false questions with one left blank

[mishima]

Homework Statement

If a test consists of 15 true false questions, in how many ways can a student mark his paper if:
a) he answers each question
b) he leaves anyone question unanswered.

Homework Equations

Multiplication of choices

The Attempt at a Solution

a) 2^15 Correct.
b) 3*(2^14) Incorrect. (right answer = 245,760)
One question has 3 choices, the rest have 2?

 

[mishima]

Also made a tree diagram up to question 4, showing the pattern 3, 8, 20, 48.

 

[LCKurtz]

Homework Statement

If a test consists of 15 true false questions, in how many ways can a student mark his paper if:
a) he answers each question
b) he leaves anyone question unanswered.

Homework Equations

Multiplication of choices

The Attempt at a Solution

a) 2^15 Correct.
b) 3*(2^14) Incorrect. (right answer = 245,760)
One question has 3 choices, the rest have 2?

Don't forget you have 15 choices for which question to not answer.

 

[mishima]

Ah, okay so it's as if you make one selection out of 15, then you have 14 to pick 2 from...so

15*(2^14)

Thank you.

 

[mishima]

My tree diagram was also set up incorrectly, correct sequence would be 1, 4, 12, 24 for up to 4 questions.