A bank PIN is a string of four digits, each digit 0-9. (a) How many choices are there for a PIN if the last digit must be odd? Make sure to explain your answer. (b) How many choices are there for a PIN if the last digit must be odd and all the digits must be different from each other? Make sure to explain your answer.

a) 5,000 b) 3,600

Step-by-step explanation:

a) there are four different slots, and for the first three slots there are a possibility for 10 different numbers and in the last slot there can only be 5 different numbers. So you get 10 x 10 x 10 x 5 which leaves you with 5,000 possibilities

b) the same thing as above but know you have fewer numbers 10 x 9 x 8 x5 which gives you 3,600 possibilities