How Many Possible Committees Can Be Chosen from a Group of 8 Men and 9 Women?

In summary, "Another counting problem" is a mathematical problem that involves determining the number of possible outcomes or arrangements of a given set of objects or events. It is important because it has many real-world applications and helps develop critical thinking and problem-solving skills. There are different types of "Another counting problem", such as permutations and combinations, and the approach to solving it depends on the specific problem and its context. It can have multiple solutions due to different approaches or interpretations of the problem. Careful consideration of the context and assumptions is necessary to determine the most appropriate solution.
  • #1
duki
264
0

Homework Statement



A committee of seven is to be chosen from 8 men and 9 women.
a) how many possible committees are there?
b) how many committees contain at least 6 woment?
c) if bob and alice cannot be on the same committee because they cannot work together well, how many committees are possible?

Homework Equations





The Attempt at a Solution



Not sure where to start really... other than writing down every possible committee
 
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  • #2
Hints:

(a) This is a combination, (8+9) choose 7.

(b) (committee of 7 with 6 women) + (committee of 7 with 7 women)

(c) (all committees) - (those with both Bob and Alice).

--Elucidus
 

FAQ: How Many Possible Committees Can Be Chosen from a Group of 8 Men and 9 Women?

What is "Another counting problem"?

"Another counting problem" is a mathematical problem that involves determining the number of possible outcomes or arrangements of a given set of objects or events.

Why is "Another counting problem" important?

"Another counting problem" is important because it has many real-world applications, such as in probability and statistics, computer science, and economics. It also helps develop critical thinking and problem-solving skills.

What are some common types of "Another counting problem"?

Some common types of "Another counting problem" include permutations, combinations, and binomial coefficients. These problems involve determining the number of ways to arrange or select objects from a given set.

How do you approach solving "Another counting problem"?

The approach to solving "Another counting problem" depends on the specific problem and its context. Generally, it involves identifying the type of problem and then using relevant counting principles and techniques, such as the multiplication principle or the binomial theorem.

Can "Another counting problem" have multiple solutions?

Yes, "Another counting problem" can have multiple solutions. This is because there may be different approaches or interpretations of the problem, and each may lead to a different solution. It is important to carefully consider the context and assumptions of the problem to determine the most appropriate solution.

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