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
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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