Mary needs a new lock for her bike since her last one was st

Mary needs a new lock for her bike since her last one was stolen. There are 4 slots numbered 0 to 9, and Mary randomly selects a combination. What is the probability that she gets:

(a) A combination that only includes even numbers?

(b) A combination such that the first number is not 0 and all four numbers are different?

(c) A combination that has at least one 4 or at least one 5

Solution

We have 4 slots to fill with random numbers 0 to 9
a)
A combination only includes even numbers, a number is even when it ends with 0,2,4,6,8

A combination we choose must end with any of this, picking a number that ends as such = 7*8*9*5 because , we first fill the end choice,possible left are (0,2,4,6,8) i.e 5, & for the second last, we have possible choice of 9 & so on for the next digit..

Possible combinations are = 7*8*9*5 = 2520 [ With out Repetation ]

With Repetation = 10*10*10*5 = 5000

B)
Combination first number is not zero = 9*10^3 = 9000