Undergraduate probability These notes are based on A First Course in Probability Theory , 6th edition, by S. Ross. 1. Combinatorics. The ﬁrst basic principle is to multiply. Suppose we have 4 shirts of 4 diﬀerent colors and 3 pants of diﬀerent colors. How many possibilities are there? For each shirt there are 3 possibilities, so altogether there are 4 × 3 = 12 possibilities. Example. How many license plates of 3 letters followed by 3 numbers are possible? Answer. (26) 3 (10) 3 , because there are 26 possibilities for the ﬁrst place, 26 for the second, 26 for the third, 10 for the fourth, 10 for the ﬁfth, and 10 for the sixth. We multiply. How many ways can one arrange a,b,c ? One can have abc, acb, bac, bca, cab, cba. There are 3 possibilities for the ﬁrst position. Once we have chosen the ﬁrst position, there are 2 possibilities for the second position, and once we have chosen the ﬁrst two possibilities, there is only 1 choice left for the third. So there are 3 × 2 × 1 = 3! arrangements. In general, if there are
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This note was uploaded on 12/29/2011 for the course MATH 317 taught by Professor Wen during the Spring '09 term at SUNY Stony Brook.