Data 605 Discussion 6

Exercise 7

7 Five people get on an elevator that stops at five floors. Assuming that each has an equal probability of going to any one floor, find the probability that they all get off at different floors.

# Define the total number of floors and people
num_floors <- 5
num_people <- 5

# Define the factorial function
factorial <- function(n) {
  if (n == 0 || n == 1) {
    return(1)
  } else {
    return(n * factorial(n-1))
  }
}

# Calculate the total number of ways they can get off at any floor
total_ways <- num_floors^num_people

# Calculate the number of ways they can all get off at different floors (permutations)
favorable_ways <- factorial(num_people)

# Calculate the probability
probability <- favorable_ways / total_ways

# Print the probability
print(probability)

## [1] 0.0384

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