How many words, each of 3 vowels and 2 consonants, can be formed from the letters of the word ‘INVOLUTE’?
How many words, each of 3 vowels and 2 consonants, can be formed from the letters of the word ‘INVOLUTE’?
How many words, each of 3 vowels and 2 consonants, can be formed from the letters of the word ‘INVOLUTE’?
Answer : In the word ‘INVOLUTE’ there are 4 vowels, ‘I’,’O’,’U’ and ‘E’ and there are 4 consonants, ‘N’,’V’,’L’ and ‘T’. 3 vowels out of 4 vowels can be chosen in 4C3ways. 2 consonants out of 4 consonants can be chosen in 4C2 ways. Length of the formed words will be [3 + 2] = 5. So, the 5 letters can be written in 5! Ways. Therefore, the total number of words can be formed is = [4C3 X 4C2 X 5!] = 2880.
The word is 'INVOLUTE'
Number of consonants = 4
Number of vowels = 4.
The words formed should contain 3 vowels and 2 consonants.
The problems becomes:
[i] Select 3 vowels out of 4.
[ii] Select two consonants out of 4. Number of selections =
[iii] Arrange the five letters [3 vowels + 2 consonants] to form words.
Number of permutations = 5!
[iv] Apply fundamental principle of counting:
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- Permutations and Combinations
- Mathematics
- How many words can be formed with 3 vowels and 2 consonants taken from the word equation?
- How many words can be formed by using 3 vowels and 2 consonants selecting from the letters of the word involute?
- How many words of 2 vowels and 3 consonants each can be formed with the letters of the word daughter?
- How many 5 letter words can be formed containing 3 vowels and 2 consonants?
- How many words of 2 consonants and 2 vowels can be formed?
- How many words of 3 consonants and 3 vowels can be formed?
Number of words formed =
=
= 4 x 6 x 120 = 2880
Hence, the number of words formed = 2880
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How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
There are 4 vowels and 4 consonants in the word INVOLUTE.
Out of these, 3 vowels and 2 consonants can be chosen in \[\left[ {}^4 C_3 \times^4 C_2 \right]\] ways.
The 5 letters that have been selected can be arranged in 5! ways.
∴ Required number of words =\[\left[ {}^4 C_3 \times {}^4 C_2 \right] \times 5! = 4 \times 6 \times 120 = 2880\]
Concept: Factorial N [N!] Permutations and Combinations
Is there an error in this question or solution?
How many words can be formed with 3 vowels and 2 consonants taken from the word equation?
Required number of ways =2880.
How many words can be formed by using 3 vowels and 2 consonants selecting from the letters of the word involute?
of words that can be formed containing 3 vowels and 2 consonants chosen from 'INVOLUTE' is 2880.
How many words of 2 vowels and 3 consonants each can be formed with the letters of the word daughter?
Therefore, 30 words can be formed from the letters of the word DAUGHTER each containing 2 vowels and 3 consonants.
How many 5 letter words can be formed containing 3 vowels and 2 consonants?
1440`. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
How many words of 2 consonants and 2 vowels can be formed?
Hence , 72 words can be formed.
How many words of 3 consonants and 3 vowels can be formed?
Total no. of words = 4C1×13=52.