Q) Find the number of words that can be made by arranging the letters of the word "INTERMEDIATE" so that the order of vowels do not change?

Asked by araima2001 | 29th Nov, 2016, 09:47: PM

Expert Answer:

begin mathsize 18px style Vowels space equals space straight a space straight e space straight i space straight o space straight u space space space space space space space
In space the space given space word comma space INTERMEDIATE
number space of space vowels space equals space 3 space but space occuring space in space 6 space places space in space the space word
number space of space consonants space equals space 6 space
Total space number space of space letters space equals space 12 space
The space consonant space apostrophe straight T apostrophe space is space repeated space twice
So comma space total space number space of space words space formed space such space that space the space order space of space the space vowels space is space not space changed space equals space fraction numerator 12 factorial over denominator 6 factorial space 2 factorial end fraction equals 332640 end style

Answered by Rebecca Fernandes | 30th Nov, 2016, 02:23: PM