Question

Find the number of permutations of the word "AUROBINDO" in which vowels appear in an alphabetical order.

Answer 1

Choose any one of the remaining consonants.

It would have 5 possible places to go relative to the 4 vowels.

Once that consonant is in place, another consonant has 6 places to go.

The 3rd consonant has 7 places to go, and the last consonant has 8 places to go.

There are then $5\times 6\times 7\times 8=1,680$ ways.