Question

I am seeing a few different answers for this question, so I would like to confirm the correct one. Please don't copy from the other ones on here as I am trying to get the correct answer. Thanks!

A student is required to answer 10 out of 13 questions. Find the number of possible choices if the student must answer:

(b) the first or second question, but not both

Answer 1

Given,

A student is required to answer 10 out of 13 questions.

Initially the student has 13C10 choices = 286 choices different choices or ways of answering

Now,

If the student has to answer the first question and not the second question, then he / she has to answer 9 questions from remaining 11 and that can be done in (1 x 11C9) ways = 55 ways / choices

Similarly, If the student has to answer the second question without answering the first question, then he / she has to answer 9 questions from remaining 11 and that can be done in (1 x 11C9) ways = 55 ways / choices

So, total number of choices a student has if the student has to answer first or second question but not both = 55 + 55 = 110