# The combination to a lock consists of a sequence of three

Last updated: 8/8/2022

The combination to a lock consists of a sequence of three numbers in the range 0-42. a) How many combinations are possible in which no two consecutive numbers can be the same? b) How many combinations are possible in which all three numbers are different? c) What is the probability that the combination of a randomly-chosen lock consists of three different numbers? d) What is the probability that the combination of a randomly-chosen lock contains at least one repeated number? a) If no two consecutive numbers can be the same, write the expression (consisting of a product of numbers) that represents the number of possible combinations. ___ (Do not simplify.) Thus, if no two consecutive numbers can be the same, the number of combinations is ___ (Simplify your answer.) b) If all three numbers are different, the number of combinations is ___ (Simplify your answer.) c) The probability that the combination of a randomly-chosen lock consists of three different numbers is. ___ (Round to two decimal places as needed.) d) The probability that the combination of a randomly-chosen lock contains a repeated number is ___ (Round to two decimal places as needed.)