A fourdigit number is formed by randomly selecting four digi

A four-digit number is formed by randomly selecting four digits, without replacement, from the set D = {1,2,3,4,5,6,7}.

What is the probability that the resulting number is greater than 4200?

Solution

There are 7 digits here.

Thus, there are 7P4 = 840 ways to choose a 4-digit number.

For a number to be greater than 4200, the first digit must be 4 or more.

Case 1: If the first digit is 4, the second digit must be 2 or more, there are 5 ways to do that. Then 5 ways to get the third, and 4 ways to get the fourth. There are 1*5*5*4 = 100 ways so that the first digit id 4.

Case 2: If the first digit is 5 or more, there are 3 ways for the first digit, 6 ways for the second, 5 ways for the third, 4 ways for the fourth. Hence, there are 3*6*5*4 = 360.

Thus, there are a total of 100+360 = 460 ways.

Thus,

P(greater than 4200) = 460/840 = 0.547619048 [ANSWER]