In how many ways can be the letters of the word ELEEMOSYNARY be arranged so that the S is always immediately followed by a Y?
Attempt: There are 3 Es, and 2 Ys, and and then all letters appear once including the S. There are 12 letters in total
Then assume SY is a letter, then there will be 10 letters. Then the word can ELEEMOSYNARY can be arranged in 10!/{3!7(1!)}.
Please can someone please help me. I keep getting the wrong answer.
Thank you.
Best Answer
Here's how to attempt this problem.
Assume that the S and the Y are always together, meaning they form "one" letter.
Now we have that there are $11$ letters. Also, note that there is only technically $1$ Y, since the "letter" SY is included now. Now, we have that:
$$\frac{11!}{3!1!} $$