The English alphabet has 5 vowels and 21 cons | vedclass

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Question

(A) Step $1$: Select $2$ different vowels from $5$ available vowels. The number of ways is $^{5}C_{2} = \frac{5 	imes 4}{2 	imes 1} = 10$.Step $2$:

Vedclass · Accepted Answer

$50400$

Vedclass · Answer

(A) Step $1$: Select $2$ different vowels from $5$ available vowels. The number of ways is $^{5}C_{2} = \frac{5 	imes 4}{2 	imes 1} = 10$.Step $2$: Select $2$ different consonants from $21$ available consonants. The number of ways is $^{21}C_{2} = \frac{21 	imes 20}{2 	imes 1} = 210$.Step $3$: The total number of combinations of $2$ vowels and $2$ consonants is $10 	imes 210 = 2100$.Step $4$: Each combination consists of $4$ distinct letters,which can be arranged in $4!$ ways. $4! = 4 	imes 3 	imes 2 	imes 1 = 24$.Step $5$: The total number of words that can be formed is $2100 	imes 24 = 50400$.

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

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