Question

How many different 9-0 letter code words can be made using the symbols %, %, %, %, &, &, &, +, +?

Answer 1

1260

Explanation:

There are 4 percent signs, 3 ampersands, and 2 plus signs.

If each symbol were different, we'd be able to make `9!` code words (there'd be 9 choices to put in the first position, 8 in the second, 7 in the third, and so on, giving `9xx8xx7xx6xx5xx4xx3xx2xx1=9! = 362,880`

However, we have to take out the internal ordering of each repeated symbol (this will get rid of duplicates). There are `4!` to order the percent signs, `3!` to order the ampersands, and `2!` to do the plus signs. And so we get:

`(9!)/(4!3!2!)=(362,880)/(24xx6xx2)=1260`