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The English alphabets has 5 vowels …

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

    • Posted by Shreya Purohit 8 years, 3 months ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Zainam Algaz 8 years, 3 months ago

    2 vowels can be chosen in 5C25C2 ways 2 consonants can be chosen in 21C221C2 ways 4 letters can be arranged in 4! ways ∴∴ The number of words consisting of 2 vowels and 2 consonants ⇒5C2×21C2×4!⇒5C2×21C2×4! ⇒5×41×2×21×201×2⇒5×41×2×21×201×2×24×24 ⇒10×210×24⇒10×210×24 ⇒50400

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