Contents
 • one choice • many choices: permutations • many choices: combinations • many choices: combinations • independent events • dependent events • permutations without repettitions • permutations with identical elements • combinations • coditional probabilities • and or events • two outcomes • total probability theorem • Bayes rule • union sets and probability • fundamental counting principle

 Other exercices

 Combinatorics - Probability
Example6: Dependent events

Dependent events
combinations

Many choices: Dependent events

We need 4 books. One book of Mathematics, one book of Physics, one book of Chemistry, and one book of Biology. Because we do not have enough money to buy all of them at once, we decide to buy one after another book. How many possibilities do we have to buy these books?

We can choose the book of Mathematics (BM) first, then the book of Biology (BB), the book of Physics (BP), and the book of Chemistry (BC), in this order. We have the following possibilities:

BM first: 6 possibilities
BM -- BB -- BP -- BC
BM -- BB -- BC -- BP
BM -- BP -- BB -- BC
BM -- BP -- BC -- BB
BM -- BC -- BP -- BB
BM -- BC -- BB -- BP

Similarly, we have 6 possibilities for BB, BP, and BC.
The total of possibilities is 4 x 6 = 24 = 4! = (total number of books)! = 24.

This kind of problems involve dependent events ( choosing a book takes an order, thus affect its following choice). Rach event is simply obtained by permutation. Let's remember that with permutations, the order is important.

Other opprach:
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The first 6 possibilities for BM are shown in the following tree diagram:

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