An admission test given by a university contains 10 true-false questions. Eight or more of the questions must be answered correctly in order to be admitted.
(a) How many different ways can the answer sheet be filled out?
(b) How many different ways can the answer sheet be filled out so that 8 or more questions are answered correctly?
a) If for each question there are only 2 options--yes or no then 10 questions can have 2^10=1024 possible ways.
b) We can simply count the 3 ...
This solves two questions regarding a true-false test and the possible ways to fill it out.