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.
[iii] Arrange the five letters [3 vowels + 2 consonants] to form words.
Number of permutations = 5!
[iv] Apply fundamental principle of counting:
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
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