Question

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

Answer 1

Answer: 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,

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

Answer 2

The number of different words that can be made by rearranging the letters in each given word, including the original word, are as follows:

1. Vector: 6! = 720 different words.
2. Trust: 5! = 120 different words.
3. Caravan: 7! = 5,040 different words.
4. Closeness: 9! = 362,880 different words.
5. Mathematical: 13! = 6,227,020,800 different words.

The number of different words that can be formed by rearranging the letters of a word is given by the factorial of the number of distinct letters in the word. The formula for factorial is n! = n × (n-1) × (n-2) × ... × 2 × 1.

For "Vector," there are 6 distinct letters, so the number of different words is 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

For "Trust," there are 5 distinct letters, so the number of different words is 5! = 5 × 4 × 3 × 2 × 1 = 120.

For "Caravan," there are 7 distinct letters, so the number of different words is 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040.

For "Closeness," there are 9 distinct letters, so the number of different words is 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880.

For "Mathematical," there are 13 distinct letters, so the number of different words is 13! = 13 × 12 × 11 × ... × 3 × 2 × 1 = 6,227,020,800.

These calculations include the original word as one of the possibilities.