Probability and Permutations in PIN Numbers

The video tutorial explains how to calculate the probability of selecting a five-digit PIN with no repeated digits. It begins by determining the total number of possible PINs with repetition, which is 100,000. Then, it calculates the number of PINs without repetition using both a step-by-step method and permutations, resulting in 30,240 PINs. The probability is found by dividing the non-repeating PINs by the total, yielding a probability of 30.24%. The tutorial also demonstrates using a calculator to verify the permutation calculation.

What is the main problem discussed in the video?

• Finding the probability of a PIN with repeated digits

• Calculating the total number of PINs

• Determining the probability of a PIN with no repeated digits

• Understanding the concept of permutations

How many ways are there to select each digit in a five-digit PIN when repetition is allowed?

• 6 ways

• 9 ways

• 5 ways

• 10 ways

What is the total number of possible five-digit PINs when repetition is allowed?

• 10,000

• 100,000

• 1,000,000

• 50,000

How many ways are there to select the second digit in a five-digit PIN when repetition is not allowed?

• 7 ways

• 8 ways

• 9 ways

• 10 ways

What is the total number of five-digit PINs with no repeated digits?

• 30,000

• 100,000

• 10,000

• 30,240

What is the probability of a five-digit PIN having no repeated digits?

• 0.4024

• 0.6024

• 0.5024

• 0.3024

What percentage represents the probability of a PIN with no repeated digits?

• 50.24%

• 40.24%

• 30.24%

• 20.24%

What mathematical concept can be used to determine the number of PINs without repetition?

• Multiplication

• Division

• Permutation

• Combination

What is the formula for permutations of n things taken r at a time?

• n divided by r

• n times r

• n permute r

• n choose r

How can the probability of a PIN with no repeated digits be quickly calculated using permutations?

• By adding 10 permute 5 to 10 to the fifth

• By multiplying 10 permute 5 by 10 to the fifth

• By dividing 10 permute 5 by 10 to the fifth

• By dividing 10 permute 5 by 10 to the fourth