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 = \( 2100\times 4!=50400\)
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