How many different words can be made from the given word by rearranging the letters? (The given word is also counted.) Vector
Trust
Caravan
Closeness
Mathematical

Here we'll use Permutations, nPr,

where n = total number of letters,

r = total number of letters you are picking, in your case, you are picking all the letters so it would be, nPn,

Step-by-step explanation:

"Vector" has 6 letters so 6P6 = 720

"Trust" has 5 letters so 5P5 = 120

"Caravan" has 7 letters so 7P7 = 5040

"Closeness" has 9 letters so 9P9 = 362880

"Mathematical" has 12 letters so 12P12 = 479001600

Consider the provided equation:

Substitute the x = 2, in the above equation.

Substitute the x = 3, in the above equation.

Substitute the x = 4, in the above equation.

Substitute the x = 5, in the above equation.

Substitute the x = 6, in the above equation.

Now, consider the equation .

Substitute the x = 2, in the above equation.

Substitute the x = 3, in the above equation.

Substitute the x = 4, in the above equation.

Substitute the x = 5, in the above equation.

Substitute the x = 6, in the above equation.

Therefore, the complete table is shown in the figure 1: