There are 24 permutations.The number of permutations of 4 objects taken 4 at a time is given by4!/(4-4)! = 4!/0! = 4!/1 = 4! = 24

4P3 = 24In a permutation order matters.You can also think about it in this way; you have 3 spots to fill,the first spot you have 4 items to choose from. Now there are only 3 items left to choose for the next spot. There are only 2 items left for the third spot, so4 * 3 * 2 = 24Letter A

The correct option is (a) 12.

You are watching: How many permutations exist of the letters a, b, c, d taken four at a time?

Step-by-step explanation: We are given to find the number of permutations that exists for the letters a, b, c and d taking two at a time.

We know

The number of permutations of "n" different things taking "r" ("r" less than or equal to "n") at a time is given by the formula:

*

In the given case, there are 4 different letters and we are to take two at a time, so

n = 4 and r = 2.

Therefore, the number of permutations will be

*

Thus, there are 12 permutations that exists.

Option (a) is correct.



Answer from: carson5238

A. 24

Step-by-step explanation:

We are asked to find the number of permutations exist of the letters a, b, c, d taken four at a time.

We will use permutation formula to solve our given problem.

*
, where,

n = Total number of objects,

r = Number of objects taken at a time.

We can see total number of letters is 4 and number of letters taken at a time is also 4, so substituting these values in permutation formula we will get,

*

*

*

*

*

*

Therefore, 24 permutations exist for our given letters and option A is the correct choices.



Answer from: emmaraeschool

A. 24

Step-by-step explanation:

We are asked to find the number of permutations exist of the letters a, b, c, d taken four at a time.

We will use permutation formula to solve our given problem.

*
, where,

n = Total number of objects,

r = Number of objects taken at a time.

We can see total number of letters is 4 and number of letters taken at a time is also 4, so substituting these values in permutation formula we will get,

*

*

*

*

*

*

Therefore, 24 permutations exist for our given letters and option A is the correct choices.



Answer from: michellealvarez985

Option A. 24

Step-by-step explanation:

There are four letters a, b, c, d and we have to tell the permutations made when taken 3 at a time.

This phenomenon exist =

*
=
*

=

*
= 4! = 4 × 3 × 2× 1 = 24

Therefore, option (A) 24 are the permutations exist.


Answer from: allieballey0727
The answer is 24 permutations. You can solve this by looking at how many ways we can choose the first letter, second letter... and so on, depending on how many you take at a time (in this case, four at a time).(4 possible letters) x (3 possible letters) x (2 possible letters) x (1 remaining letter) = 24Or in other words 4! (4 factorial).
Answer from: Parmenter
The answer to this is A, 244*3*2*1=24 
Answer from: mfox793
The correct answer is 24You have to apply factorials here and formulas. You have 4 letters which means that your n=4, and you have 3 objects at a time which, means that you have 4 different groups of combinations with 6 permutations in each due to the 3! factorial. 6 x 4 is 24.
Answer from: Keo247
The correct answer is A) 244*3*2*1=24

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