Question

You own 15 CDs. You want to randomly arrange 8 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?

The probability that the CDs are in alphabetical order is ?

A bag contains 9 red marbles, 7 white marbles, and 8 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that all the marbles are red?

The probability that all the marbles are red is .

What is the probability that exactly two of the marbles are red?

The probability that exactly two of the marbles are red is .

What is the probability that none of the marbles are red?

The probability of picking no red marbles is

Answer 1

Solution:-

1) The probability that the CDs are in alphabetical order is 1/¹⁵P₈ = 1/ 259459200

2)

total number of possibilites = 24C3

a)

probability that all marbles are red = 9C3 / 24C3 = 84/2024 = 0.0415

b)

required probability = 9C2*15C1 / 24C3 = (36*15)/2024 = 0.2668

c)

required probability = 15C3 / 24C3 = 455/2024 = 0.2248