There room 24 permutations.The number of permutations that 4 objects bring away 4 in ~ a time is offered by4!/(4-4)! = 4!/0! = 4!/1 = 4! = 24

4P3 = 24In a permutation order matters.You can additionally think about it in this way; you have actually 3 spots to fill,the an initial spot you have 4 items to select from. Now there are just 3 items left to select for the following spot. There are just 2 item left for the third spot, so4 * 3 * 2 = 24Letter A

The correct choice 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: us are provided to discover the variety of permutations that exists because that the letter a, b, c and d taking two at a time.

We know

The variety of permutations that "n" different things acquisition "r" ("r" much less than or equal to "n") in ~ a time is provided by the formula:

In the offered case, there room 4 different letters and also we are to take 2 at a time, so

n = 4 and also r = 2.

Therefore, the variety of permutations will be

Thus, there room 12 permutations the exists.

Option (a) is correct.

A. 24

Step-by-step explanation:

We space asked to uncover the variety of permutations exist that the letters a, b, c, d taken four at a time.

We will use permutation formula to resolve our offered problem.

, where,

n = Total number of objects,

r = number of objects taken in ~ a time.

We deserve to see total variety of letters is 4 and variety of letters taken at a time is additionally 4, so substituting these values in permutation formula we will get,

Therefore, 24 permutations exist because that our given letters and option A is the exactly choices.

A. 24

Step-by-step explanation:

We space asked to uncover the number of permutations exist the the letter a, b, c, d taken 4 at a time.

We will use permutation formula to resolve our given problem.

, where,

n = Total number of objects,

r = number of objects taken in ~ a time.

We have the right to see total variety of letters is 4 and number of letters taken in ~ a time is likewise 4, for this reason substituting these values in permutation formula we will certainly get,

Therefore, 24 permutations exist because that our offered letters and option A is the exactly choices.

Option A. 24

Step-by-step explanation:

There are four letters a, b, c, d and also we need to tell the permutations made as soon as taken 3 at a time.

This phenomenon exist =

=

=

= 4! = 4 × 3 × 2× 1 = 24

Therefore, choice (A) 24 space the permutations exist.

The price is 24 permutations. You can solve this by looking at how numerous ways we can select the first letter, second letter... And so on, relying on how plenty of you take it at a time (in this case, four at a time).(4 feasible letters) x (3 possible letters) x (2 possible letters) x (1 remaining letter) = 24Or in various other words 4! (4 factorial).
The answer to this is A, 244*3*2*1=24
The correct answer is 24You have to use factorials here and also formulas. You have 4 letters which way that your n=4, and you have actually 3 objects at a time which, method that you have 4 various groups that combinations v 6 permutations in each due to the 3! factorial. 6 x 4 is 24.
The exactly answer is A) 244*3*2*1=24

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