Permutations/Combinations

[nenny]

I'm really, really lost with this stuff. I understand the idea behind it, and the formulas, but there's something about the word problems that confuses me to no end. Anyway, I need help with a couple of questions, and god knows my teacher is never available outside of class


"The director of a high school all-state orchestra has identified 8 classical selections and 10 popular selections from which he must choose 6 selections for the concert."

a) How many ways can he select AND arrange the music for the concert program if he wants to perform 4 classical selections and 2 popular selections, and the program must begin and end with the popular selections?

(I had 151200 for this part, but I'm second guessing the way I answered it)

b) How many ways can he select AND arrange the music for the concert program if he wants 4 classical selections and 2 popular selections, and there must be at least one classical selection between the two popular selections?

(I have *no* clue on this one...)



Any help would be wonderful.. thanks!!

 

[Unco]

G'day,

"The director of a high school all-state orchestra has identified 8 classical selections and 10 popular selections from which he must choose 6 selections for the concert."

a) How many ways can he select AND arrange the music for the concert program if he wants to perform 4 classical selections and 2 popular selections, and the program must begin and end with the popular selections?

(I had 151200 for this part, but I'm second guessing the way I answered it)

What are your thoughts on this....

There are six slots:

• pop cla cla cla cla pop

There are 10 choose 2 ways to select the pops.
There are 2! ways to place the two pops.

There are 8 choose 4 ways to select the clas.
There are 4! ways to place the four clas.

I have an exam on this in a week and a bit's time so anyone please feel free to critique this.

 

[pka]

If I understand this correctly, you correct in the part a.

For part b) I get \(\displaystyle \left( {_5 C_2 } \right)\left( {_8 C_4 } \right)\left( {_{10} C_2 } \right)\left( {4!} \right)(2!)\)


Most of that you can figure out.
The combination of 5 taken 2 comes from the fact:
_C_C_C_C_ the classical pieces make 5 places to put the popular pieces.