Question

How many different 10-letter words (real or imaginary) can be formed from the following letters? O, Z, Q, Y, N, U, Z, J, W, V ten-letter words (real or imaginary) can be formed with the given letters. (Type a whole number.)

Answer 1

Answer: 1814400

Step-by-step explanation:

The given letters : O, Z, Q, Y, N, U, Z, J, W, V

Number of letters = 10

Here Z is repeated two times.

The number of permutations of n things , where a are repeated items , b are repeated items  and so on :-

$\dfrac{n!}{a!\ b!\ ....}$

Then, the number of ten letter words can be formed by given 10 letters , where Z is repeated 2 times :-

$\dfrac{10!}{2!}=\dfrac{3628800}{2}=1814400$

Hence, the number of different 10-letter words (real or imaginary) can be formed =1814400