From a team of 8 students, 3 are attending a meeting.
You are watching: How many different committees of 7 people can be formed from a group of 10 people?
Quantity A: The variety of different groups that can attend amongst the 8 students
Quantity B: 336
Explanation:
To resolve this problem, friend would need to utilize the combination formula, which is





336 would certainly be the result of computing the permutation, which would certainly be not correct in this case.
Michael own 10 paintings. Michael would prefer to hang a single painting in each of five different rooms. How many different ways are there because that Michael to cave 5 the his 10 paintings?





Explanation:
This trouble involves the permutation that 10 items throughout 5 slots. The an initial slot (room) have the right to have 10 different paintings, the 2nd slot can have 9 (one is already in the first room), the 3rd slot can have 8 and also so on. The number of possibilities is acquired by multiply the number of possible options in each of the 5 slots together, which right here is

Explanation:
There are



A restaurant has actually a meal distinct that allows you to pick one of three salads, one of five sandwiches, and also two of fifteen next dishes. How many feasible combinations room there because that the meal?
Explanation:
Although this is a permutation layout problem, we have to be careful regarding the last portion (i.e. The next dishes). We understand that our meal will certainly have:
(3 feasible salads) * (5 feasible sandwiches) * (x possible combinations of next dishes).
We have to ascertain how countless side dishes can be selected. Now, it does not matter what stimulate we placed together the next dishes, therefore we have to use the combinations formula:
c(n,r) = (n!) / ((n-r)! * (r!))
Plugging in, we get: c(15,2) = 15! / (13! * 2!) = 15 * 14 / 2 = 15 * 7 = 105
Using this in the equation above, we get: 3 * 5 * 105 = 1575
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Example inquiry #21 : Permutation / mix
The President has actually to choose from six members of congress to offer on a committee of three possible members. How numerous different groups of three can he choose?
Possible Answers:
9
120
20
60
Correct answer:
20
Explanation:
This is a combinations difficulty which method order does no matter. For his an initial choice the chairman can pick from 6, the second 5, and also the third 4 therefore you might think the prize is 6 * 5 * 4, or 120; but this would be the prize if that were choosing an ordered collection like angry president, secretary of state, and also chief that staff. In this case order does no matter, therefore you should divide the 6 * 5 * 4 through 3 * 2 * 1, because that the 3 seats he is choosing. The answer is 120/6, or 20.
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Example inquiry #21 : Permutation / mix
Mohammed is being treated to ice cream cream because that his birthday, and he"s allowed to build a three-scoop sundae from any of the thirty-one easily accessible flavors, v the only condition being the each of these spices be unique. He"s also permitted to pick


Knowing these details, how numerous sundae combinations space available?
Possible Answers:
Correct answer:

Explanation:
Because bespeak is not crucial in this problem (i.e. Cacao chip, pecan, butterscotch is no various than pecan, butterscotch, cacao chip), the is handle with combinations fairly than permutations.
The formula because that a mix is given as:

where


For the ice cream choices, there are thirty-one alternatives to construct a three-scoop sundae. So, the number of ice cream combine is provided as:

Now, for the topping combinations, we are told there room ten alternatives and that Mohammed is allowed to pick two items; however, us are additionally told that Mohammed has currently chosen one, therefore this pipeline nine options with one item gift selected:

So there are 9 "combinations" (using the word a little bit loosely) obtainable for the toppings. This is maybe intuitive, however it"s precious doing the math.
Now, to discover the total sundae combinations—ice cream and toppings both—we main point these two totals:
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Example question #23 : Permutation / combination
If there space


Possible Answers:
Correct answer:

Explanation:
To solve this problem, we must recognize the concept of combination/permutations. A combination is supplied when the bespeak doesn"t issue while a permutation is used when order matters. In this problem, the two class representatives space randomly chosen, therefore it doesn"t matter what bespeak the representative is favored in, the end an outcome is the same. The basic formula because that combinations is



Plugging in choosing 2 human being from a group of 20, us find



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Example question #24 : Permutation / combination
There space eight feasible flavors that curry in ~ a certain restaurant.
Quantity A: variety of possible combinations if four distinct curries are selected.
Quantity B: variety of possible combine if five unique curries room selected.
Possible Answers:
Quantity B is greater.
The two amounts are equal
Quantity A is greater.
The connection cannot it is in determined.
Correct answer:
Quantity A is greater.
Explanation:
The variety of potential combinations for



Quantity A:

Quantity B:

Quantity A is greater.
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Example inquiry #12 : exactly how To find The greatest Or Least variety of Combinations
Quantity A: The variety of possible combinations if four unique options are make from ten possible options.
Quantity B: The variety of possible permutations if two unique selections are made from ten possible options.
Possible Answers:
The connection cannot it is in established.
Quantity B is greater.
Quantity A is greater.
The two quantities are equal.
Correct answer:
Quantity A is greater.
Explanation:
For



And the number of potential permutations (order matters) is

Quantity A:

Quantity B:

Quantity A is greater.
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Example concern #26 : Permutation / combination
There space

Possible Answers:
Correct answer:

Explanation:
When taking care of combinations, the variety of possible combinations once selecting



For quantity A, the variety of combinations is:


For amount B, the variety of combinations is:


Quantity B is greater.
See more: How To Make A Buttonhole With A Brother Sewing Machine, How To Create A Buttonhole
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