Problem: a certain roller coaster has 3 cars , and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 3 times , what is the probability that the passenger will ride in each of the 3 cars ?
Rationale: "probability = ( favorable cases ) / ( total number of cases ) total number of ways in which a person can ride car = 3 * 3 * 3 = 27 ( in first ride he has 3 options to sit , in second right again he has 3 seats available to sit and so on ) number of favorable cases , i . e . , when he rides on different cars ; he can choose seat car in 3 ways in his 1 st ride . he can choose seat car in 2 ways in his 2 nd ride . he can choose seat car in 1 ways in his 3 rd ride . so , 3 * 2 * 1 = 6 ways thus , probability of choosing different seats = 6 / 27 = 2 / 9 answer : c"
annotated_formula: multiply(factorial(3), power(divide(1, 3), 3))