Providefull solutionsfor each of the following.

1. You have downloaded 20 new songs onto yourphone as shown in the table.

Artist Number of Songs

A Tribe Called Red 3

Drake 8

The Weeknd 7

Alessia Cara 2

Assuming order does not matter, if you randomly play 8 from your new list of downloaded songs, what is the probability, without evaluating, that you will hear:

1. no A Tribe Called Red songs?
2. exactly three Drake songs or exactly four Drake songs?
3. two songs from each artist?
4. at least one The Weeknd song?

A password has to use the following format: LDDDDLLL, where L can be any of the upper case letters in the alphabet, and D can be any digit including 0. None of the digits or letters can repeat.

1. What is the probability that a random password uses only vowels (A,E,I,O,U) and odd numbers (1,3,5,7,9)?Show work but do not evaluate.
2. What is theprobability that the password spells the word"MATH?"Show work but do not evaluate.

Our class is creating a new academic team, the Data Managers. The team will have 4 members to perform different tasks: collector, analyser, grapher, and recorder. 10 people in class want to be on the team, so we pick a random team out of the 10.

1. If exactly 4 boys volunteer, what is the probability that the team is all boys or no boys?Evaluate your answer.
2. What is the probability that Student 1 and Student 2 are on the team? Evaluate your answer.
3. With two teacher coaches, the team of four takes a picture (6 people in picture). What is the probability that the teachers are together in the picture?Evaluate your answer.

data mangement