14111cn6.12-15 - c Kendra Kilmer Section 6.4 Arrangements...

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c Kendra Kilmer September 16, 2011 Section 6.4 - Arrangements and Combinations Example 1: Suppose we want to seat 12 people in a row of 12 seats. How many arrangements are possible? The above product is called a factorial : n ! = n ( n - 1 )( n - 2 ) ··· 3 · 2 · 1 Note: 0! = 1 Example 2: How many ways can we select 5 people from a group of 12 and arrange them in 5 chairs? Definition: If we have n distinct elements and we want to take r of them in an arrangement, we say that the number of arrangements of n things taken r at a time is: Example 3: How many ways can we select 25 people from a group of 35 and arrange them in 25 chairs? Arrangement of n objects, not all distinct: Given a set of n objects in which n 1 are alike of one kind, n 2 are alike of another, ... , n r alike of another so that n 1 + n 2 + ··· + n r = n then the number of arrangements of the n objects taken n at a time is: Example 4: Suppose we have 2 identical red marbles, 3 identical green marbles, and 1 blue marble. If we want to line the marbles up in a row, how many distinguishable arrangements of the 6 marbles are there?
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