Math Is Fun Forum

Danbee

Member

Registered: 2008-08-28

Posts: 21

Permutations and combinations

A bookshelf contains six mysteries and three biographies. In how may ways can two books be selected so that at least one of the books is a mystery book?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Permutations and combinations

View it in two discrete steps:

ignoring the biographies, how many ways can you choose 2 of the six mystery books?

6C2 = 15 ways, we are finding the number of combinations rather than permutations; since obviously the order of selection is not important.

ontop of this, if you pick on mystery book; you can pair it up with one of 3 biography books so you also have

6×3 = 18 ways  (3 ways of combing a single mystery, 6 different mystery books)

so the total is 33 ways, doing it by brute force you have mystery books ABCDEF, and biographies 123

AB,AC,AD,AE,AF,BC,BD,BE,BF,CD,CE,CF,DE,DF,EF = 15
A1,A2,A3,B1,B2,B3,C1,C2,C3,D1,D2,D3,E1,E2,E3,F1,F2,F3 = 18

33 ways

Last edited by luca-deltodesco (2008-11-06 04:52:53)

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Danbee

Member

Registered: 2008-08-28

Posts: 21

Re: Permutations and combinations

U are right!
Thanks