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Of a group of 10 PTA members, a committee will be selected t
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30 Dec 2017, 14:25
30 Dec 2017, 14:25
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Of a group of 10 PTA members, a committee will be selected that has 1 president and 3 other members. How many different committees could be selected?
Drill 2
Question: 4
Page: 563
Question: 4
Page: 563
Show: :: OA
840
Re: Of a group of 10 PTA members, a committee will be selected t
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08 Jan 2018, 16:27
08 Jan 2018, 16:27
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Explanation
There are 10 possible presidents.
After the president is selected, there are 9 members left to fill the remaining 3 spots. Order does not matter, so the number of possibilities for the other three spots is \(\frac{9 \times 8 \times 7}{3 \times 2 \times 1}\) . Simplifying the fraction yields 3 × 4 × 7 = 84.
So, there are 10 possible presidents and 84 possible committees for each president. Multiplying them yields the total number of possible committees, 840.
There are 10 possible presidents.
After the president is selected, there are 9 members left to fill the remaining 3 spots. Order does not matter, so the number of possibilities for the other three spots is \(\frac{9 \times 8 \times 7}{3 \times 2 \times 1}\) . Simplifying the fraction yields 3 × 4 × 7 = 84.
So, there are 10 possible presidents and 84 possible committees for each president. Multiplying them yields the total number of possible committees, 840.
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Of a group of 10 PTA members, a committee will be selected t
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29 Jan 2018, 17:40
29 Jan 2018, 17:40
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sandy wrote:
Of a group of 10 PTA members, a committee will be selected that has 1 president and 3 other members. How many different committees could be selected?
Take the task of creating the committee and break it into stages.
Stage 1: Select a person to be president.
We can choose any of the 10 PTA members, so we can complete stage 1 in 10 ways
Stage 2: Select the 3 other members
Since the order in which we select the 3 other members does not matter, we can use combinations.
We can select 3 people from the remaining 9 people in 9C3 ways (84 ways)
So, we can complete stage 2 in 84 ways
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create the 4-person committee) in (10)(84) ways (= 840 ways)
Answer: 840
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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