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1. How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant?
The first three letters can be either consonants or vowels. So, each of them have 26 options.
Note that the question asks you to find out the number of distinct initials and not initials where the letters are distinct.
Hence, required answer
= 26 × 26 × 26 × 21
= 263 × 21
Solution:
The last of the four letter words should be a consonant. Therefore, there are 21 options.The first three letters can be either consonants or vowels. So, each of them have 26 options.
Note that the question asks you to find out the number of distinct initials and not initials where the letters are distinct.
Hence, required answer
= 26 × 26 × 26 × 21
= 263 × 21