GRE Math aid » Arithmetic » Permutation / combination » how to uncover the best or least variety of combinations

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

*
.

*
 is the variety of possibilities, 
*
is the variety of students, and 
*
is the students attending the meeting. Thus,
*
.

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 

*
various permutations the 3 people from a group of 7 (when stimulate matters). Over there are 
*
possible ways to arrange 3 people. For this reason when order doesn"t matter, there can be 
*
various committees formed. 


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 

*
 different toppings of the available 
*
, return he"s already decided well in development that one of them is going to be peanut butter cup pieces.

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 

*
 is the number of options and 
*
 is the dimension of the combination.

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

*
 students in a class and
*
 people room randomly choosen to become class representatives, how numerous different ways can the representatives be chosen?


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 

*
, where 
*
 is the number of things you have actually and 
*
 is the things you desire to combine.

 

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

*
. As such there space a
*
 different ways to pick the
*
 class representatives.


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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 

*
 selections make from 
*
 possible alternatives is

*

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 

*
 choices made from 
*
 possible options, the variety of potential combinations (order does no matter) is

*

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 flavor alternatives at an ice cream shop.


Possible Answers:
Correct answer:

*


Explanation:

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

*
 choices out of 
*
 options is:

*

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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