I have to arrange the word ALGEBRA but vowels must maintain their original relative order. So I thought we have 3 spaces if we put vowels like A_ _ E _ _ A (I know there are 3! ways to arrange those) but how do I approach the problem about consonants?
Could someone help me?
Best Answer
Imagine Alice, Elizabeth, and Anne standing in that order. Now send Larry to join them. He can fit in any of $4$ positions. Next send George, who can fit in any of $5$ positions, then Bruce, who'll have $6$ choices of where to fit, and finally Roscoe, who'll have $7$ choices. The total number of orderings is thus
$$4\cdot5\cdot6\cdot7=840$$
It doesn't really matter in what order you send the guys; the first guy will have $4$ choices, the next guy $5$, and so on.