Randomly pick a number from the set containing numbers betwe

Randomly pick a number from the set containing numbers between 1000-9999 such that the digits are not repeated. Justify your answer to the following questions:

(c) What is the probability that its first digit is 1 or its last two digits are 20?

Solution

P(first digit 1) = 1*10*10*10=1000

P(last 2 digits 20) = 9*10*1*1=90

P(both) = 1*10*1*1=10

hence, answer= 1000+90-10 = 1080