Assume that there are 13 board members: 8 females, and 5 males including Larry. There are 4 tasks to be assigned. Note that assigning the same people different tasks constitutes a different assignment.
(1) Find the probability that both males and females are given a task.
(2) Find the probability that Larry and at least one female are given tasks.

- Pulsified333

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- Pulsified333

@jim_thompson5910

- jim_thompson5910

what do you have so far?

- Pulsified333

I have one of the answers right but I don't know which is right
1) 15360/17160
2) 864/17160

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## More answers

- jim_thompson5910

let me think

- Pulsified333

ok

- jim_thompson5910

so it says that exactly one of your answers is correct?

- Pulsified333

yeah I just don't know which

- jim_thompson5910

hmm strange. I'm not getting either but I probably made a mistake somewhere. Let me double check

- Pulsified333

I think the first one is right though

- jim_thompson5910

this is what I keep getting
m = male
f = female
problem (1)
3 m, 1 f = (5 npr 3)*(8 npr 1) = 480
2 m, 2 f = (5 npr 2)*(8 npr 2) = 1120
1 m, 3 f = (5 npr 1)*(8 npr 3) = 1680
total = 480+1120+1680 = 3280
# of outcomes = 13 npr 4 = 17160
probability = 3280/17160
Problem (2)
Larry + 2 m + 1 f = (4)*(4 npr 2)*(8 npr 1) = 384
Larry + 1 m + 2 f = (4)*(4 npr 1)*(8 npr 2) = 896
Larry + 0 m + 3 f = (4)*(4 npr 0)*(8 npr 3) = 1344
total = 384+896+1344 = 2624
# of outcomes = 13 npr 4 = 17160
probability = 2624/17160

- Pulsified333

For number 1 I got 17160-(1680+120)

- jim_thompson5910

why did you compute it like that?

- Pulsified333

https://answers.yahoo.com/question/index?qid=20110131185103AA6hK3T

- Pulsified333

I followed this and I got that first answer but i don't understand how to do number 2

- Pulsified333

I remember now it was the second one thats wrong

- jim_thompson5910

ah I see now, that's a better way to do #1

- jim_thompson5910

why not determine the number of ways to have Larry + 3 males
then subtract that result from the total (17160) to figure out how many ways to have Larry + at least one female

- Pulsified333

so how would you do that

- jim_thompson5910

how many ways are there to assign tasks to Larry and 3 other males?

- Pulsified333

40

- jim_thompson5910

how did you get 40?

- Pulsified333

well if larry has task A then that one thing. Then lets say he gets task B, that is different than task A

- Pulsified333

so isnt there 4 different tasks that larry could be assigned

- jim_thompson5910

so he has 4 choices, yes

- Pulsified333

C(5,3)*4

- jim_thompson5910

5-1 = 4 males left
4-1 = 3 slots left
Compute P(4,3)

- Pulsified333

oh

- Pulsified333

24?

- jim_thompson5910

then you multiply that by 4
4*P(4,3) = 4*24 = 96

- jim_thompson5910

there are 96 ways to pick Larry + 3 other males

- Pulsified333

okay so 17160-96?

- jim_thompson5910

hmm now that I think about it, that computes the number of ways to pick everything the opposite of "Larry + 3 other males" so larry is left out. Let me rethink

- jim_thompson5910

did you see how I did problem 2 above? I'm guessing that answer didn't work?

- Pulsified333

I didn't try it yet

- Pulsified333

but yes I saw how you did it

- jim_thompson5910

give it a try. It's probably wrong but I initially thought it was the correct way to do it

- Pulsified333

well i only have 4 attempts left so

- Pulsified333

look at how this person did number two for a similar but not the same problem http://www.jiskha.com/display.cgi?id=1236051521

- Pulsified333

@satellite73

- Pulsified333

I have no clue how to find the second answer

- Pulsified333

@dan815

- Pulsified333

@jim_thompson5910 i have no clue how to find the second answer

- jim_thompson5910

same here. I'm still trying to decipher what that other poster wrote

- jim_thompson5910

there are (13 npr 4) - (12 npr 4) = 5,280 ways to have 4 people chosen where Larry is one of the 4 people

- jim_thompson5910

as for the other piece, hmm, I'm thinking there are
(12 npr 3) - (4 npr 3) = 1,296 ways to pick at least one female

- jim_thompson5910

so maybe we multiply the results to get 5,280*1,296 = 6,842,880
that result seems way too big though

- Pulsified333

it is because its bigger than the total number of ways

- jim_thompson5910

good point

- Pulsified333

I found it :D 216/715

- jim_thompson5910

I'm curious as to how you got that

- Pulsified333

My friend helped me with that so he's gonna explain it to me tomorrow thank you for trying though

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