How many $5$ letter arrangements can be made from the word “numeracy” if it MUST include the letter “$y$”? What I’ve done so far- I know that $y$ will occupy one spot of $5$ letters.
I also know that I have to multiply by $5$ to get the final answer.
However, I don’t know how to proceed to find the value of y when it is any slot.
Can anybody help me answer this one?

First, forget the y in numeracy and find the number of ways to pick $4$ letters from numerac. There are $7 \choose 4$ ways, or $35$. Each way can be rearranged $4! =24$ times, so the total number of arrangements is $35*24 =840$. Now, look at an example $4$-letter arrangement NUME. You can put a Y in the following spaces in _ N _ U _ M _ E _ to make a $5$-letter word with Y. There are $5$ spaces, so you multiply $840*5$ to get $4200$ ways.
