There are eight magazines, including 4 fashion books and 4 sports books. If three books are to be selected at random without replacement, what is the probability that at least one fashion book will be selected?
When you see the word "at least", always think the complement. Instead of looking for the probability that at least one fashion book will be selected, look for the probability no fashion book will be selected. Once you find that probability, subtract that from 1 to get your final answer.
# of ways to select 3 books from 8 books: 8C3 = 8!/(3!*5!) = 56
# of ways of not selecting any fashion book is selecting 3 sports book: 4C3 = 4
Probability of no fashion book = 4/56 = 1/14
Probability of at least 1 fashion book = 1 - 1/14 = 13/14
