Which to Use: Permutation or Combination for Arranging Company Directors?

In summary, the conversation discusses a question related to statistics about arranging directors for a photo. The first question involves calculating the number of ways to arrange the directors in a straight line. The second question asks for the number of ways to arrange the directors alternately by gender. The third question involves choosing a committee with at least 2 women, and the difference between permutations and combinations is also mentioned. The conversation ends with the clarification that the first question involves permutations.
  • #1
ibysaiyan
442
0
idk if i should post this question here as i couldn't find any specific forum to post at homework section this has to do with statistics. the question is:

Question: The Board of a company consists of 4 men and 4 women.The 8 directors are to stand in a straight line so that a photo can be taken.
a)calculate the number of difft. ways in which the 8 directors can be arranged in a line.
b)in how many ways can the directors be arranged so that in the line the men and women stand alternately.
c) 5 members of the board of directors are to be chosen to form a committee .there must be atleast 2 women in the committee.find the number of different committee that could be chosen.

=( confused sos pls, could some1 guide me thro as where to use npr or npc.tyvm in advance and if i have posted the wrong place could the moderators shift it to its appropriate place
 
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  • #2
The big difference is whether order is respected. You have to ask yourself, if you change the order of two arrangements/committtes/lists/pools/groups/tables/etc, are they still the same? Permutations are used when changing the order means the things are no longer equal. Combinations are used when changing the order has no effect on the equality.
 
  • #3
k, so how shall i start with the 1st bit?so would the 1st one be permutation?
 
  • #4
I would say so.
 
  • #5
k,ty
 

What is the difference between permutation and combination?

Permutation and combination are both ways of arranging a set of objects. The main difference between them is that permutation involves the order in which the objects are arranged, while combination does not. In other words, permutation considers the arrangement of objects as distinct, while combination considers them as the same.

How do I calculate the number of permutations or combinations?

The formula for calculating permutations is nPr = n!/(n-r)!, where n is the total number of objects and r is the number of objects being arranged. For combinations, the formula is nCr = n!/((n-r)! * r!). In both cases, the exclamation mark (!) represents the factorial function, which means multiplying a number by all the numbers below it. Alternatively, you can use a calculator or an online permutation and combination calculator to find the answer.

What is the use of permutations and combinations in real life?

Permutations and combinations are used in various fields such as mathematics, statistics, and computer science. In real life, they are used to solve problems related to arrangements, probability, and combinations. For example, in a lottery, the winning numbers are a combination of a few numbers chosen from a larger set of numbers. Similarly, in a game of cards, the different combinations of cards can determine the winner.

Can I have repetitions in permutations and combinations?

Yes, you can have repetitions in permutations and combinations. In permutations with repetitions, the same object can be used more than once in an arrangement. For example, in the word "MISSISSIPPI," the letter S is repeated four times, so the number of permutations would be 11!/4!. In combinations with repetitions, the same object can be selected more than once. For instance, in a game of picking candies from a jar, you can pick the same candy more than once.

How can I identify whether I need to use permutations or combinations to solve a problem?

To determine whether to use permutations or combinations, you need to consider if the order of objects matters in the problem. If the order matters, use permutations. If the order does not matter, use combinations. Additionally, you should also check if repetitions are allowed in the problem. If repetitions are allowed, use permutations with repetitions or combinations with repetitions, depending on the situation.

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