When buying a new car, you have a choice of 4 different models, 3 different colors, and either compact or family size. How many choices are there for one car?
A. 5
B. 12
C. 16
D. 24
There are 20 entries in the chess tournament. How many ways can they finish in first, second, and third place?
A. 340
B. 6,840
C. 7,220
D. 8,350
Answer (2)
1 ) 4 d i ff ere n t m o d e l s , 3 d i ff ere n t co l ors an d 2 s i zes 4 ⋅ 3 ⋅ 2 = 24 ( c h o i ces ) 17. 20 e n t r i es in t h e c h ess t o u r nam . 20 − t h e n u mb er o f w a ys t o se l ec t 1. pl a ces 19 − t h e n u mb er o f w a ys t o se l ec t 2. pl a ces 18 − t h e n u mb er o f w a ys t o se l ec t 3. pl a ces t h e n u mb er o f w a ys t o se l ec t t h e t o p t h ree = 20 ⋅ 19 ⋅ 18 = 6 , 840
The total number of choices for one car is 24, which corresponds to option D. For the chess tournament, the total number of ways the 20 participants can finish in first, second, and third places is 6,840, which corresponds to option B.
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