173
THe number of arrangements of the letters of the word "MULTIPLE" that can be made preserving the order in which the vowels (U,I,E) occur and not counting the original attangement is:
1. 6719
2. 3359
3. 6720
4. 3214
173
THe number of arrangements of the letters of the word "MULTIPLE" that can be made preserving the order in which the vowels (U,I,E) occur and not counting the original attangement is:
1. 6719
2. 3359
3. 6720
4. 3214
Out of the 8 possible positions, we choose 3 in order to place vowels U, I, E, and we have C(3,3) ways of choosing the vowels, i.e. only one way - their required order. Then we arrange the remaining in 5!/2! (we divide by 2! because of the repetition of letter L) and then we subtract 1, as required by the question.
That is,
C*(8,3)*C(3,3)*5!/2! -1 = 3359.