How many words, with or without meaning, each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE? is it right write it as 4p3*4p2
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→In the word INVOLUTE, there are 4 vowels, namely, I,O,E,U and 4 consonants, namely, N, V, L and T.
→The number of ways of selecting 3 vowels out of 4 = 4C3 = 4.
→The number of ways of selecting 2 consonants out of 4 = 4C2 = 6.
⇒Therefore, the number of combinations of 3 vowels and 2 consonants is 4 × 6 = 24.
⇒Now, each of these 24 combinations has 5 letters which can be arranged among themselves in 5 ! ways.
→Therefore, the required number of different words is 24 × 5 ! = 2880.
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