How many words can be formed from the letters of the word, TRIANGLE? How many of these will begin with `T` and end with `E ?`

Explanation

(i) The given word 'TRIANGLE' contains 8 letters.
Total number of words formed with these 8 letters
`= ""^(8)P_(8)=8! =40320.`
Hence, the required number of words `= 40320.`
(ii) By fixing T in the beginning and E at the end the remaining 6 letters can be arranged among themselves in ` ""^(6)P_(6)=6! =720` ways.
Hence, the total number of words, each beginning with T and ending with E = 720.