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How many ways can 4 people be chosen from a group of 9. tell whether the situation is a permutation or combination then solve?
Wiki User
∙ 14y ago
This situation is a combination, since from a group of 9 people, 4 are chosen and the order in which they are chosen is not important. So we have
9C4 = (9 x 8 x 7 x 6 )/(4 x 3 x 2 x 1) = 126.
The following explanation will tell you why we got this result.
The first person can be any one of 9.
The second person can be any one of the remaining 8.
The third person can be any one of the remaining 7.
The fourth person can be any one of the remaining 6.
The number of ways to make this choice of 4 people is (9 x 8 x 7 x 6) = 3,024.
This is a permutation, and that's what the question asked for when it asked ... "How many ways ... ".
But not all of the groups chosen in these 3,024 ways are different groups. In fact, each different
group will show up 24 times, because 4 people can be arranged (4 x 3 x 2 x 1) = 24 ways.
So the number of combinations, i.e. different groups of 4 people, is (3,024 / 24) = 126.
Wiki User
∙ 14y ago
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Is this a permutation In how many different ways could a committee of 5 students be chosen from a class of 25 students?
6,375,600
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The grouping of a subset of a set of items where the order does not matter is called a combination. One such example is the UK's National Lotto where 6 numbers have to be chosen from the 59 numbers 1-59).If there are n different items and a subset of r of them are chosen where the order of choosing does not matter then the number of combinations is given by:nCr = n!/((n-r)!r!)where n! means "n factorial" - the product of all numbers 1 × 2 × ... × n; 0! is defined to be 1.--------------------------------------------------------------------------------------------------------------------------------Where the order of selection does matter, it is called a permutation. One such example would be the order of the first three runners in a race.If there are n different items and a subset of r of them are chosen where the order of choosing does matter, then the number of permutations is given by:nPr = n!/(n-r)!
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How many ways can a committee of 4 people be chosen from 10 people?
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it is a combination: 9!/4!=9 x 8 x 7 x 6
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6,375,600
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How many different two letter arrangements can you make without repeating letters?
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In case of digits or numbers, when we say combination, since the order of the numbers matters, we really need to find the permutations. For example, 12 and 21 are two permutations and not combination. The permutation for 10 digits chosen 5 ways is 10*9*8*7*6, which is 30240. But how many are there in whole like four digit has 24.
There are 20 students participating in a math bee How many ways can the students be chosen to go first second third and fourth?
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A committee consists of 7 women and 4men if a member of the committee is chosen at random to act as chairperson what is the probability that the choices is woman?
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A jury of 12 people is selected from a pool of 30 people that includes 12 men and 18 women what is the probablilty that the jury will be composed of 12 women?
Order does not matter in this case because the order in which the 12 women are chosen won't change the answer. Since order does not matter, a combination is used instead of a permutation. Therefore the equation would be set up as: (18 C 12) / (30 C 12) = 0.02% The numerator is achieved because there are 18 women of the 30 people and 12 women are chosen. The denominator is achieved because there are 30 people in all and 12 people are chosen from those 30 people. Hope this helped!
