In how many ways can a committee of 5 be selected from 35 members?

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In summary, the total number of combinations for selecting a committee of 5 from 35 members is 324,632. This is different from a permutation, where the order does matter. The probability of selecting a specific committee is 1/324,632 or approximately 0.0003%. The number of possible combinations can change if the number of members or the size of the committee is different. The concept of combinations can be applied in real-life situations such as selecting a jury, forming a team, or creating a menu.
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diceyfume
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In how many ways can a committee of 5 be selected from 35 members?
 
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This won't work, diceyfume.

You are obviously refusing to utilize your intellect, and are only interested in being spoonfed "answers".

I strongly advise you to quit maths, because your attitude makes you incompetent in it.
 

1. How many total combinations are possible for selecting a committee of 5 from a group of 35 members?

The total number of combinations for selecting a committee of 5 from 35 members is 35 choose 5, which can be calculated using the combination formula nCr = n! / (r!(n-r)!). In this case, n = 35 and r = 5, so the calculation is 35! / (5!(35-5)!) = 35! / (5!30!) = (35*34*33*32*31) / (5*4*3*2*1) = 324,632.

2. How is this selection process different from a permutation?

A combination is a selection of items from a group where the order does not matter, while a permutation is a selection where the order does matter. In this case, selecting a committee of 5 from 35 members is a combination because the order in which the members are chosen does not affect the final result. However, if the committee was required to have a specific president, vice president, secretary, etc., then it would be a permutation.

3. What is the probability of selecting a specific committee of 5 from 35 members?

The probability of selecting a specific committee of 5 from 35 members is 1/324,632 or approximately 0.0003%. This can be calculated by dividing the number of ways to select the specific committee (1) by the total number of combinations (324,632).

4. Can the number of possible combinations change if the number of members or the size of the committee is different?

Yes, the number of possible combinations will change if either the number of members or the size of the committee is different. The total number of combinations can be calculated using the formula nCr = n! / (r!(n-r)!), where n is the number of members and r is the size of the committee. So, if either n or r changes, the total number of combinations will also change.

5. How can this concept of combinations be applied in real-life situations?

The concept of combinations can be applied in various real-life situations, such as selecting a jury for a trial, forming a team in sports, or creating a menu for a restaurant. In each of these situations, a specific number of people or items need to be selected from a larger group, and the order in which they are chosen does not affect the final result.

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