(i) Find the number of four-letter words that can be formed from the letters of the word HISTORY. (Each letter to be used at most once).
(ii) How many of them contains only consonants.
(iii) How many of them begin and end in a consonant.
(iv) How many of them begin with a vowel.
(v) How many contains the letters \( Y \).
(vi) How many begin with \( \mathrm{T} \) and end in a vowel.
(vii) How many begin with \( \mathrm{T} \) and also contain \( \mathrm{S} \).
(viii) How many contain both vowels.
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