In how many ways can the letters of the word chromatic be arranged

a. without any restrictions
b. if the position of the vowels can’t change
c. find the probability that the string of letters begins with the letter m

a. without any restrictions
since there 9 letters in the word CHROMATIC, then the number of ways it can be arrange is
P = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x1
P = 362880 ways can the word CHROMATIC be arranged with no restirction

B. if the position of the vowels can’t change
since there are 6 consonant letters in the word CHROMATIC, then the number of ways it can be arrange without changing the vowel is:
P = 6 x 5 x 4 x 3 x2 x 1
P = 720 ways