• Welcome! The new FreeMathHelp.com forum is live. We've moved from VB4 to Xenforo 2.1 as our underlying software. Hopefully you find the upgrade to be a positive change. Please feel free to reach out as issues arise -- things will be a little different, and minor issues will no doubt crop up.

In how many ways....

aburchett

New member
Joined
Jan 19, 2011
Messages
48
In how many different ways can the top eight new indie bands be ranked on a top eight list? The top hit song for each of the eight bands will compete to receive monetary awards of $1000, $500, $250 and $100, respectively. In how many ways can the awards be given out?

My work:
In how many different ways can the top eight new indie bands be ranked on a top eight list?
P[sub:16992ywf]8[/sub:16992ywf][sub:16992ywf],[/sub:16992ywf][sub:16992ywf]8[/sub:16992ywf] = 8!/(8-8)! = 8!/0! = 8*7*6*5*4*3*2*1/1 = 40,320
The top eight new indie bands can be ranked on a top eight list 40,320 different ways.

In how many ways can the awards be given out?
8_C_4 = 8!/(8-4)! = 8!/4! = 8*7*6*5*4!/4! = 1,680
The awards can be given out 1,680 different ways.

Is this correct?
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Hello, aburchett!

Correct answers . . . just one typo.


In how many different ways can the top eight new indie bands be ranked on a Top Eight list?

The top hit song for each of the eight bands will compete to receive monetary awards of $1000, $500, $250 and $100, respectively.
In how many ways can the awards be given out?


My work:

In how many different ways can the top eight new indie bands be ranked on a top eight list?

\(\displaystyle P(8,8) \,=\, \text{8!}{0!} \,=\,\frac{ 8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{1} \:=\: 40,320\)

The top eight new indie bands can be ranked on a Top Eight list on 40,320 different ways. .
Right!


In how many ways can the awards be given out?

\(\displaystyle _8C_4 \:=\: \frac{8!}{(8-4)!} \:=\: \frac{8!}{4!} \:=\: \frac{8\cdot7\cdot6\cdot5\cdot4!}{4!} \:=\: 1,680\)
. \(\displaystyle \uparrow\)

You mean P

The awards can be given out 1,680 different ways. .
Yes!
 
Top