1. 8.3 notes December 21, 2012
8.3 Combinations
In permutations, order is important.
Questions involving arrangements of letters, digits,
or people in positions are always permutation questions.
Sometimes we wish to just find how many ways to
"choose" objects without arranging them.
Look at the difference between the next 2 examples.
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2. 8.3 notes December 21, 2012
Example 1) How many ways can you choose a student council
of President, Vice­President, Secretary, and Treasurer out of
9 candidates?
Example 2) How many ways can I choose a committee of 4 people
out of 9 people?
In this example the choice of Tom, Joe, Sue, Betty is
no different that Joe, Betty, Tom, Sue.
How many ways can you arrange the SAME 4 people?
Therefore we modify the Permutation formula to produce the
answer to this COMBINATION question.
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3. 8.3 notes December 21, 2012
If order does NOT matter, then we have a
COMBINATION.
The formula for combinations is:
n Cr =
The r! in the denominator is the arrangements
of the identical items which is no longer
important.
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4. 8.3 notes December 21, 2012
Calculate the following (without a calculator):
8 C2 = 8 C6 =
7 C3 = 7 C4 =
What do you notice? This should make sense
when you look at the formula.
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5. 8.3 notes December 21, 2012
Therefore, what would 14 C3 equal?
14 C11
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6. 8.3 notes December 21, 2012
Combination Question Practice:
1)
2)
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7. 8.3 notes December 21, 2012
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8. 8.3 notes December 21, 2012
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9. 8.3 notes December 21, 2012
FINAL THOUGHT: Should it be called a
COMBINATION LOCK ???
HOMEWORK:
Supplementary sheet, next page.
Page 727 #4,5a)c), 9, 10, 13,
14, 15a)c)
mult. ch. #1,3.
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