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 $4 = C(4,3) = 4$. The number of ways of selecting $2$ consonants out of $4 = C(4,2) = 6$. Therefore, the number of combinations of $3$ vowels and $2$ consonants is $4+6=10$.
Now, each of these $10$ combinations has $5$ letters which can be arranged among themselves in $5!$ ways. Therefore, the required number of different words is $10\times5! = 1200$.
But the answer is $2880$.
What am I doing wrong? Please explain.