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?

Asked by Abhisek | 1 year ago |  131

##### Solution :-

Given: 2 vowels and 2 consonants should be selected from the English alphabet. We know that, there are 5 vowels.

Thus, number of ways of selecting 2 vowels out of 5

$$^5C_2=\dfrac{5!}{3!2!}=10$$

Also we know that, there are 21 consonants.

Thus, number of ways of selecting 2 consonants out of 21

$$^{21}C_2=\dfrac{21!}{19!2!}=210$$

Thus, total number of combinations of selecting 2 vowels and 2 consonants is

$$10\times 210=2100$$

Every 2100 combination consists of 4 letters, which can be arranged in 4! ways.

Therefore, number of words = $$2100\times 4!=50400$$

Answered by Pragya Singh | 1 year ago

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