Q.6    The English alphabet has 5 vowels and 21 consonants. How many words with
           two different vowels and 2 different consonants can be formed from the
           alphabet?

Answers (1)
S seema garhwal

Two different vowels and 2 different consonants are to be selected from the English alphabets.

Since there are 5 different vowels so the number of ways of selecting two different vowels = ^5C_2

                                                                                                                                      =\frac{5!}{2!3!}=10

Since there are 21 different consonants so the number of ways of selecting two different consonants = ^2^1C_2

                                                                                                                                      =\frac{21!}{2!19!}=210

Therefore, the number of combinations of 2 vowels and 2 consonants =10\times 210=2100

Each of these 2100 combinations has 4 letters and these 4 letters arrange among themselves in 4! ways.

Hence, the required number of words =210\times 4!=50400

 

 

                                                                                                                                        

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