How many different combinations?

Question

Johnny must answer 15 questions, each question only has 2 answer choices (A or B). Johnny must then rank each of his 15 answers in order of confidence 1 to 15, using each number exactly once.

 

Example: Q1 = A and ranked 15, Q2 = B and ranked 14, etc...

 

How many different combinations are there?

 

Answer 1

With 15 questions, and 2 choices each, ignoring the ranking, there are 2¹⁵ possible choices.

Ignoring the 2 choices, with 15 rankings, there are 15! ways to rank the set of questions.

 

To combine the two, multiply the numbers of possibilities. It's a reaaaaally large number.