Hi,

If anyone can please check what I have done, that would be awesome,

62.

**Class rings:** You want to purchase a class ring. The ring can be made from three different metals, six different designs, and twelve stones. How many different class rings are possible? 216 class rings are possible.

I used the fundamental counting principal. 12*3*6=216 different rings.

Mr F says: Correct.
64.

**Photography:** A photographer lines up 15 members of a family in a single line in order to take a single photograph. How many different ways can the photographer arrange the family for the picture?

The photographer can arrange the family in 225 different ways because he wants them in a single line for a single photograph. There are 15 family members, and 15^2= 225 different ways.

Mr F says: Incorrect. It's 15! ways.
66.

**Music:** The window of a music store has eight stands in a fixed position where instruments can be displayed. In how many ways can three identical guitars, two identical keyboards, and three identical violins be displayed?

I used the fundamental counting principal, and got 18. 3*2*3=18 But I know that's not right because the instruments are identical, it's not like they're different. Is the answer 3?

Mr F says: No. The answer is $\displaystyle {\color{red} \frac{8!}{3! \cdot 2! \cdot 3!}}$.
Thank you very much

Isabel