Consider 2 vowels and 6 consonants from English alphabets. Find out how many words are possible with 2 vowels and 2 consonants?
Answers
Answer:
For solving this, we need to use the concept of combinations by separating the vowels and constants and then placing them one by one. Hence, the number of words each consisting of two vowels and two consonants which can be made out of the letters of the word 'DEVASTATION' is 1638.
Answer: 1638
Explanation:
Vowels are speech sounds which complete the pronunciation of any word. It is an essential component of any word without which a word cannot be spoken. Vowels are a, e, i, o, u
Consonant are speech sounds other than the vowels mentioned above which requires complete or partial closure of the vocal tract which is unlike that of vowels as there there is no closure of the vocal tract. There are 21 consonants i.e. b, c, d, f etc.
Infinite words can be made using vowels and consonants that we used our everyday life as well as those which we are not aware of but exists.
For instance taking the word DEVASTATION
Vowels : E A A I O
Consonants : D V A T T N
Case 1 :
AA TT
total nos.= 4!/2! 2! = 6
Case 2:
AA Other than TT
5 c2 × 4!/2! = 120
Case 3:
4 c2 ×4!/2! = 72
Case 4:
(4 c2× 5c2) × 4!= 1440
Hence, adding case 1, case 2, case 3 and case 4 we get,
6 + 120 + 72 + 1440
= 1638
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