- #1
diceyfume
- 30
- 0
In how many ways can a committee of 5 be selected from 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.
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.
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).
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.
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.