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

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.

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,