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Decide which method to use to find the number of possible outcomes. How many ways are there to select three bracelets from a box containing ten bracelets if order does not matter? For Teacher Use Only ORSPBDOK2 439120 M2L1Q1 Combination Fundamental Counting Principle Permutation

Pergunta

Decide which method to use to find the number of possible outcomes.
How many ways are there to select three bracelets from a box containing ten bracelets if order does not matter?
For Teacher Use Only
ORSPBDOK2 439120 M2L1Q1
Combination
Fundamental Counting Principle
Permutation

Decide which method to use to find the number of possible outcomes. How many ways are there to select three bracelets from a box containing ten bracelets if order does not matter? For Teacher Use Only ORSPBDOK2 439120 M2L1Q1 Combination Fundamental Counting Principle Permutation

Solução

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BeckyElite · Tutor por 8 anos

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The number of ways to select three bracelets from a box containing ten bracelets, where the order does not matter, is 120.

Explicação

## Step 1<br />The problem involves selecting three bracelets from a box containing ten bracelets, where the order of selection does not matter. This is a classic example of a combination problem.<br /><br />## Step 2<br />A combination is a selection of items from a larger set where the order of selection does not matter. In this case, the order in which the bracelets are selected does not matter, so we use the combination method.<br /><br />## Step 3<br />The formula for combinations is given by:<br />### \(C(n, r) = \frac{n!}{r!(n-r)!}\)<br />where \(n\) is the total number of items, \(r\) is the number of items to choose, and \(!\) denotes factorial.<br /><br />## Step 4<br />In this problem, \(n = 10\) (the total number of bracelets) and \(r = 3\) (the number of bracelets to choose).<br /><br />## Step 5<br />Substitute \(n = 10\) and \(r = 3\) into the combination formula to find the number of ways to select three bracelets from ten.
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