Thread: 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?

I have the answer:

72,072

but I don't know how to get it. Thanks to anyone who can help.

C(14,7)*c(7,5)=?

I'm sorry, what do you do?

Combination of 14 taken 7 times the combination of 7 taken 5 at a time.

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.

Hello, Averee!

A different approach . . . same answer.

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!

Okay, so what did you do with those numbers to get 72,072?

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

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.

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

I see, thank you.