Question

a passcode must have exactly 5 digits. digits cannot be repeated, the passcode must begin with an odd number and 0s cannot be used anywhere in the passcode. how many different passcodes are possible?

Answer 1

Below is the code that generates all possible passcodes and counts the number of them.

Python

# Define a function to generate all possible passcodes

def generate_passcodes():

# Initialize variables

passcodes = []

digits = [1, 2, 3, 4, 5, 6, 7, 8, 9]

# Generate all possible passcodes

for first_digit in digits[::2]: # Use slicing to only consider odd digits

for second_digit in digits[:9]:

if second_digit != first_digit:

for third_digit in digits[:9]:

if third_digit not in [first_digit, second_digit]:

for fourth_digit in digits[:9]:

if fourth_digit not in [first_digit, second_digit, third_digit]:

for fifth_digit in digits[:9]:

if fifth_digit not in [first_digit, second_digit, third_digit, fourth_digit]:

passcode = str(first_digit) + str(second_digit) + str(third_digit) + str(fourth_digit) + str(fifth_digit)

passcodes.append(passcode)

# Return the list of passcodes

return passcodes

# Generate all possible passcodes

passcodes = generate_passcodes()

# Count the number of passcodes

number_of_passcodes = len(passcodes)

# Print the number of passcodes

print(number_of_passcodes)