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Re: Of a group of 10 PTA members, a committee will be selected t
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08 Jan 2018, 16:27
1
Expert Reply
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. _________________
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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
1
Expert Reply
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.
Re: Of a group of 10 PTA members, a committee will be selected t
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07 Aug 2021, 00:47
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