How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word honesty *?

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Solution

There are 8 letters in the word DAUGHTER including 3 vowels and 5 consonants. We have to select 2 vowels out of 3 vowels and 3 consonants out of 5 consonants.∴ Number of ways of selection = 3C2×5C3=3×10=30Now each word contains 5 letters which can be arranged among themselves in 5! ways. So, total number of words = 5!×30=120×30=3600.

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Misc 1 - Chapter 7 Class 11 Permutations and Combinations (Term 2)

Last updated at Jan. 13, 2022 by

How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word honesty *?

How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word honesty *?

How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word honesty *?

How many words with or without meaning each of 2 vowels and 3 consonants can be formed from the letters of the word honesty *?

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Transcript

Misc 1 How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER? Number ways of selecting 2 vowels & 3 consonants = 3C2 × 5C3 = 3!/2!(3 − 2)! × 5!/3!(5 − 3)! = 3!/2!1! × 5!/3!2! = 30 Now, Each of these 5 letters can be arranged in 5 ways Number of arrangements = 5P5 = 5!/(5 − 5)! = 5!/0! = 5! = 5 × 4 × 3 × 2 × 1 = 120 Thus, Total number of words = Number of ways of selecting × Number of arrangements = 30 × 120 = 3600

How many words with or without means each of two vowels and three consonants honesty?

= 5! ×30=120×30=3600.

How many words can be formed each of 2 vowels and 3 consonants from the letters of the given word mathematics?

Therefore, 30 words can be formed from the letters of the word DAUGHTER each containing 2 vowels and 3 consonants. Note: A Permutation is arranging the objects in order.

How many words each containing 2 vowels and 3 consonants can be formed with the letters of dynamite?

=6800×120=816000.

How many words with or without meaning can be formed using 2 vowels and 4 consonants?

=(40320−4320)=36000.