Question

find the number of ways to arrange the letters in SYLLABLES.

Answer 1

There is a formula for this. Are you familiar with combinatorics or permutations?

Answer 2

NOPE i hate these!!

Answer 3

9!

Answer 4

NOO

Answer 5

I believe the formula is this:

n number of letters total
and z number of "repeats," where \(k_z\) is the number per letter
\[\frac{n!}{k_1!k_2!...k_z!}\]

Answer 6

9!/(3!2!)

Answer 7

YESS thats it i dont know how to solve i though

Answer 8

hmmm.....yeah the 3 Ls.

Answer 9

how many letters are in "SYLLABLES" ? 9

so n = 9

let's each letter:
"S" - there are 2 "s"s
"Y" - only 1 y
"L" - there are 3 "L"s
"A" - only 1
"B" - only 1
"E"- only 1

Answer 10

\[\Large \frac{{9!}}{{3! \cdot 2!}} = \frac{{362880}}{{12}} = 30240\]

Answer 11

these are your k values. so you get this:
\[\frac{9!}{2! * 1! * 3! * 1! * 1! * 1!}\]
of course, 1! = 1

Answer 12

does that make sense?