Question

In how many ways can the word "HOSPITAL" be arranged?

a. 924
b. 120
c. 45040
d. 40320

Answer 1

In how many ways can the word "HOSPITAL" be arranged?

- a. 924

- b. 120

- c. 45040

- d. 40320

Solution

The word "HOSPITAL" consists of 8 different letters.

We have 8 ways to pick the first letter times. Next we have 7 ways to pick the second letter times. And we have 6 ways to pick the 3rd letter and so on...

Altogether:

Number of ways = 8 * 7 * 6 * ... * 1 = 8! = 40320.

Where 8! means factorial of 8. In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.

Answer: d. 40320.