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Question
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
Solution
All the vowels are together.
Take all the vowels as 1 unit.
Remaining consonants = 6
Total number of units for arrangement = 7
Number of arrangements = `(7!)/(2!)`
(Since in the consonant’s T’ s repeated twice)
= `(1 xx 2 xx 3 xx 4 xx 5 xx 6 xx 7)/(1 xx 2)`
= 2520
Among the vowels, the number of arrangements
= `(6!)/(2! xx 3!)`
= `(1 xx 2 xx 3 xx 4 xx 5xx 6)/(1 xx 2 xx 1 xx 2 xx 3)`
= 60
∴ Total number of arrangements = 2520 × 60
= 151200
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