Question

How many permutations exist of the letters a, b, c, d taken four at a time?
A.24
B. 12
C. 4

Answer 1

The correct answer is A) 24

4*3*2*1=24

Answer 2

Answer:

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.  

$P(n,r)=\frac{n!}{(n-r)!}$, 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,

$P(4,4)=\frac{4!}{(4-4)!}$

$P(4,4)=\frac{4!}{(0)!}$

$P(4,4)=\frac{4!}{1}$

$P(4,4)=\frac{4*3*2*1}{1}$

$P(4,4)=\frac{24}{1}$

$P(4,4)=24$

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