Question

What is the number of distinct permutations that can be formed from all the letters of the word CALIFORNIA? In the supplied answer choices, ! denotes factorial.

Answer 1

Answer:

The answer is "907,200".

Explanation:

In the word CALIFORNIA, there is a total of 10 letters in which letter A and Letter I is repeated 2 times. To solve this problem we use the multinomial principle.

The multinomial distribution model shows the results of n trials where the results of each study are prescriptive. It is also known as a distribution that makes the binomial distribution generalizable.

Ex:

$\frac{10!}{2!*2!}$

$\frac{10*9*8*7*6*5*4*3*2*1}{2*1*2*1}$

$\frac{10*9*8*7*6*5*4*3*2*1}{4}$

$10*9*8*7*6*5*3*2*1=907,200$