In how many ways can the 9 letters of the word MARMALADE be

In how many ways can the 9 letters of the word MARMALADE be arranged in a row if the arrangement must start with an L or a D?

Solution

MARMALADE

There are

2 M
3 A
1 R
1 L
1 D
1 E

So, the first letter can be chosen 2 waysn L or D.

The other 8 letters can be permuted, by permutation of like objects, in 8!/(2!3!1!1!1!) = 3360 ways.

Hence, there are 2*3360 = 6720 ways [ANSWER]