1. ## Probabilty: Some Answers That Need Checking and Etc.

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.

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.

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?

Thank you very much
Isabel

2. Originally Posted by stmsnyder1
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 ${\color{red} \frac{8!}{3! \cdot 2! \cdot 3!}}$.

Thank you very much
Isabel
..