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 2 years ago
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!!!!!!!
 2 years ago
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!!!!!!!

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KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.3Well, the first one is the easiest. We just want 24choose12 or \[\binom{24}{12}=2704156\]As for the second one, do you have a guess as to what we have to do?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.3We 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?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.3Not quite. It would be just like the first problem. 10choose5 or \[\binom{10}{5}={10! \over 5!(105)!}=252\]Also, to choose 7 fiction books out of 14 total fiction, it would be 14choose7 or \[\binom{14}{7}={14! \over 7!(147)!}=3432\]

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.3Now we just need to multiply these together. Hence, the solution for part b is \[\binom{10}{5}\cdot\binom{14}{7} =864864\]

parik
 2 years ago
Best ResponseYou've already chosen the best response.01 (24c12) 2 (10c5x14c7)/24c12
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