Question

Basic probability for Discrete math problem: (I am mostly interested in part c,d,and e if you can't do them all. will rate asap)

Imagine a fictional scenario where a new area code 229 has just been assigned to Los Angeles. To request a phone number with this new area code, a computer program randomly generates a 7-digit number s1s2s3 − s4s5s6s7. That is for i = 1, 2, ... , 7, a random number generator picks a number from 0 to 9 and assigns it to si . This is an imaginary scenario. Theres no real life restriction on what number can be a phone number. For example 000 − 0000 can be a phone number.

(a) How many different phone numbers can be generated?

(b) What is the probability that 2017 is part of the phone number generated (e.g., 320 − 1789 or 454 − 2017 but not 230 − 6178)?

(c) What is the probability that the phone number contains exactly two numbers (e.g., 121 − 2112 or 588 − 5555 but not 444 − 4444)?

(d) What is the probability that the phone number contains at least two numbers?

(e) What is the probability that the phone number contains one 3, two 4’s and four 5’s (in any order)?

Answer 1