Problem Solving

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

is the answer 13/14?

Yup Shanmugam. The answer is 13/14.

i did it in a simpler way, maybe will help you cuz i think it's easy and i'm not really good at prob problems....

it asks for at least one sport mag, so we could 1-prob of not having sport (therefore only fashion mag)...

1st trial: 1/2 prob of getting a fashion mag
2nd trial: 3/7 prob of getting a fashion mag
3rd trial: 1/3 prob of getting a fashion mag

1- (1/2*3/7*1/3)= 1-1/14 =13/14...
hope it helps....

I have the same solution that of GMATQuantCoach