There are 10 streets to be named after 10 tree types.
Ash, Birch, Cedar, Elm, Fir, Maple, Oak, Pine, Spruce, and Willow.
A city planner randomly selects the street names from the list of 10 tree types.
1. Compute the probability of each of the following events.
Event A: The first street is Birch, followed by Pine and then Willow.
Event B: The first three streets are Ash, Birch, and Spruce, without regard to order.
Write your answers as fractions in simplest form.

1. 0.0014

2. 0.0083

Step-by-step explanation:

1. The probability of selecting Birch out of 10 options is 1/10

The probability of selecting Pine out of other 9 options is 1/9

The probability of selecting Willow out of other 8 options is 1/8

The total probability of selection Birch, Pine and Willow in that order is

1/10 * 1/9 * 1/8 = 1/720 = 0.0014

2. When order is disregarded, then:

The probability of selecting any one of Ash, Birch and Spruce out of 10 options is 3/10

The probability of selecting any one of the other 2 out of 9 options is 2/9

The probability of selecting the last one out of the last 8 options is 1/8

So the total probability of selecting Ash, Birch, and Spruce, without regard to order is

3/10 * 2/9 * 1/8 = 6/720 = 1/120 = 0.0083