Reordering Mathematics
Probability
Level
2
How many words can be formed out of the words "MATHEMATICS" if the vowels occupy even places ?
1209699
75000
84000
75600
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The restriction is 4 vowels occupy even places
Since no. of letters is 11, no. of even places is 5.
4 vowels can be arranged in 5P4 / 2! = 5! / 2! ways (A occurs twice )
No. of ways in which rest of the letters can be arranged = 7! / 2!*2! (M and T occur twice )
Therefore , required no. of ways = (5!/2!) * (7!/2!2!) = 75600