In how many ways can the letters of the word 'TRIANGLE' be arranged to form words beginning with
'E
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Step-by-step explanation:
The word ′′TRIANGLE′′ has 8 letters of which 3 are vowels.
∴ Total words=8!=8×7×6×5×4×3×2×1=40320
No. of words in which two vowels are together. We select two vowels and then tie them together so that we can effectively left with 7 letters and also we need to take care of internal arrangement of two vowels.
∴No. of words in which two vowels are together=3C2×7!×2!=3×7×6×5×4×3×2×1×2=30240
But, we need to include words in which three vowels are together.
∴No. of words in which three vowels are together=3C3×6!×3!=4320
∴Required no. of words =40320−30240+4320
=14400
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