# How many different ways...?

• Apr 1st 2007, 12:51 PM
Averee
How many different ways...?
Hey,

Fourteen construction workers are to be assigned to three different tasks. Seven workers are needed for mixing cement, five for laying bricks, and two for carrying the bricks to the brick layers. In how many different ways can the workers be assigned to these tasks?

72,072

but I don't know how to get it. Thanks to anyone who can help.
• Apr 1st 2007, 12:58 PM
Plato
C(14,7)*c(7,5)=?
• Apr 1st 2007, 01:01 PM
Averee
I'm sorry, what do you do?
• Apr 1st 2007, 01:14 PM
Plato
Combination of 14 taken 7 times the combination of 7 taken 5 at a time.
• Apr 1st 2007, 01:21 PM
Averee
Sorry again. I appreciate you helping me, but I still don't understand what you did. Or how to get 72,072. I'm really new to this stuff.
• Apr 1st 2007, 01:22 PM
Soroban
Hello, Averee!

A different approach . . . same answer.

Quote:

Fourteen construction workers are to be assigned to three different tasks.
Seven workers are needed for mixing cement, five for laying bricks,
and two for carrying the bricks to the brick layers.
In how many different ways can the workers be assigned to these tasks?

This is a "partitioning" of 14 people into groups of 7, 5 and 2.

. . . . . . . . . . . . . . . . . . . 14!
The number of ways is: . --------- . = . 72,072
. . . . . . . . . . . . . . . . . .7! 5! 2!

• Apr 1st 2007, 05:51 PM
Averee
Okay, so what did you do with those numbers to get 72,072?
• Apr 1st 2007, 05:55 PM
Jhevon
Quote:

Originally Posted by Averee
Okay, so what did you do with those numbers to get 72,072?

the ! means "factorial"

it is the product of all integers from 1 up to the number

so for example, 5! = 1*2*3*4*5

7! = 1*2*3*4*5*6*7

and so on

i thought for sure you would have learnt factorials for this class already, if you're getting problems like these
• Apr 1st 2007, 06:07 PM
Averee
Quote:

Originally Posted by Jhevon
the ! means "factorial"

it is the product of all integers from 1 up to the number

so for example, 5! = 1*2*3*4*5

7! = 1*2*3*4*5*6*7

and so on

i thought for sure you would have learnt factorials for this class already, if you're getting problems like these

Thanks, I see now. That would be really hard to do without a calculator though. Yeah, this is actually a problem from a practice test for a contest our school is going to and the teacher didn't really explain most of the problems. I appreciate you guys helping me though. :)
• Apr 1st 2007, 06:10 PM
Jhevon
Quote:

Originally Posted by Averee
Thanks, I see now. That would be really hard to do without a calculator though. Yeah, this is actually a problem from a practice test for a contest our school is going to and the teacher didn't really explain most of the problems. I appreciate you guys helping me though. :)

actually, most if not all scientific calulators have ! buttons as well as C(n,r) and P(n,r) buttons...
o, you said without a calc, well, yeah i guess, there are ways to simplify it though, so you only do a relatively small calculation
• Apr 1st 2007, 06:26 PM
Averee
I see, thank you.:)