Here's the question you clicked on:
raleung2
A book club offers its members a book each month for a year from a selection of 24 books. Ten of the books are biographies and 14 of the books are fiction. a. How many ways could the members select 12 books? b. What is the probability that 5 biographies and 7 fiction books will be chosen? WORK PLEASE!!!!!!!
Well, the first one is the easiest. We just want 24-choose-12 or \[\binom{24}{12}=2704156\]As for the second one, do you have a guess as to what we have to do?
We need to choose 5 biographies out of a set of 10, and choose 7 fiction from a set of 14. Can you do each of these parts separately? How many ways can I choose 5 biographies out of 10 total?
Not quite. It would be just like the first problem. 10-choose-5 or \[\binom{10}{5}={10! \over 5!(10-5)!}=252\]Also, to choose 7 fiction books out of 14 total fiction, it would be 14-choose-7 or \[\binom{14}{7}={14! \over 7!(14-7)!}=3432\]
Now we just need to multiply these together. Hence, the solution for part b is \[\binom{10}{5}\cdot\binom{14}{7} =864864\]
1 (24c12) 2 (10c5x14c7)/24c12