Find the number of ways the letters of the word "MACHINE" can be arranged so that vowels may occupy only odd positions?
A. 3! X 4!
B. 7P3 X 4!
c. 7P4 X 3!
D. None of these
Here is how I approached it:
There are three vowels (A, I, E)and four consonants (M, C, H, N). So I treat it just like a lock code problem.
- - - - - - -
1 2 3 4 5 6 7
So Letter A has 4 choices (1, 3, 5, 7)
Letter I has 3 choices (one less than letter A)
Letter E has 2 choices.
Once these three are placed.
There are 4 places remaining and 4 consonants. Which can be arranged in 4! ways.
So the total number of ways, it can be done is
4 x 3 x 2 x 4!.
or 4! X 4!
Am I correct or am I double counting somewhere? Please advise. Thank you
A. 3! X 4!
B. 7P3 X 4!
c. 7P4 X 3!
D. None of these
Here is how I approached it:
There are three vowels (A, I, E)and four consonants (M, C, H, N). So I treat it just like a lock code problem.
- - - - - - -
1 2 3 4 5 6 7
So Letter A has 4 choices (1, 3, 5, 7)
Letter I has 3 choices (one less than letter A)
Letter E has 2 choices.
Once these three are placed.
There are 4 places remaining and 4 consonants. Which can be arranged in 4! ways.
So the total number of ways, it can be done is
4 x 3 x 2 x 4!.
or 4! X 4!
Am I correct or am I double counting somewhere? Please advise. Thank you
