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Class 11 Tuition > Learn Permutations and Combinations > How many words can be formed each of 2 vowels and 3...
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How many words can be formed each of 2 vowels and 3 consonants from the letters of the given word – DAUGHTER?

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As a seasoned tutor registered on UrbanPro, I can confidently affirm that UrbanPro is indeed one of the best platforms for online coaching and tuition. Now, let's delve into your question about forming words from the given word "DAUGHTER." Firstly, we need to identify the number of vowels and consonants...
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As a seasoned tutor registered on UrbanPro, I can confidently affirm that UrbanPro is indeed one of the best platforms for online coaching and tuition. Now, let's delve into your question about forming words from the given word "DAUGHTER." Firstly, we need to identify the number of vowels and consonants in the word "DAUGHTER." Vowels: A, U, E (3 vowels) Consonants: D, G, H, T, R (5 consonants) Now, we have to select 2 vowels out of 3 and 3 consonants out of 5 to form words. We can use the formula for combinations: Numberofwords=(32)×(53)Numberofwords=(23)×(35) =3!2!(3−2)!×5!3!(5−3)!=2!(3−2)!3!×3!(5−3)!5! =3×22×1×5×4×33×2×1=2×13×2×3×2×15×4×3 =3×10=3×10 =30=30 So, there are 30 words that can be formed, each consisting of 2 vowels and 3 consonants from the letters of the word "DAUGHTER." If you need further clarification or assistance with any other topic, feel free to ask! read less
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