Questions: In a state's lottery, you can bet 3 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect 700. Complete parts (a) through (e). a. How many different selections are possible?

In a state's lottery, you can bet 3 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect 700. Complete parts (a) through (e). a. How many different selections are possible?
Transcript text: In a state's lottery, you can bet $\$ 3$ by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect $\$ 700$. Complete parts (a) through (e). a. How many different selections are possible?
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Solution

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Solution Steps

Step 1: Understand the Problem

We are asked to calculate the number of different selections possible when choosing a sequence of \(n\) digits for a lottery game, where each digit can range from 0 to 9 inclusive.

Step 2: Identify the Parameters

The given parameter is \(n = 3\), which represents the number of digits in the sequence.

Step 3: Apply the Solution Approach

The general solution approach is to use the rule of product. Since each digit in the sequence can be any of 10 possible values (0 through 9), and since the choice of each digit is independent of the others, the total number of different selections possible is \(10^n\), where \(n\) is the number of digits in the sequence.

Step 4: Perform the Calculation

Substituting the given value of \(n = 3\) into the formula, we get \(10^3 = 10^3 = 1000\).

Final Answer:

The total number of different selections possible when selecting a sequence of 3 digits, each between 0 and 9 inclusive, is \(1000\).

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