Question

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

Answer 1

vowels= I,O,U,E
consonants = N, V,L,T
total words`= (.^4C_3 .^4C_2) .^5P_5`
`= (4!)/(1!*3!)*(4!)/(2!*2!)*(5!)/(5-5)!`
`= 4 * (4*3*2)/4 * 5!`
`= 24*120`
`=2880`
answer