Question

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.

Answer 1

@jim_thompson5910

Answer 2

what do you have so far?

Answer 3

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

Answer 4

let me think

Answer 5

ok

Answer 6

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

Answer 7

yeah I just don't know which

Answer 8

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

Answer 9

I think the first one is right though

Answer 10

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

Answer 11

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

Answer 12

why did you compute it like that?

Answer 13

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

Answer 14

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

Answer 15

I remember now it was the second one thats wrong

Answer 16

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

Answer 17

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

Answer 18

so how would you do that

Answer 19

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

Answer 20

40

Answer 21

how did you get 40?

Answer 22

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

Answer 23

so isnt there 4 different tasks that larry could be assigned

Answer 24

so he has 4 choices, yes

Answer 25

C(5,3)*4

Answer 26

5-1 = 4 males left
4-1 = 3 slots left

Compute P(4,3)

Answer 27

oh

Answer 28

24?

Answer 29

then you multiply that by 4

4*P(4,3) = 4*24 = 96

Answer 30

there are 96 ways to pick Larry + 3 other males

Answer 31

okay so 17160-96?

Answer 32

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

Answer 33

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

Answer 34

I didn't try it yet

Answer 35

but yes I saw how you did it

Answer 36

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

Answer 37

well i only have 4 attempts left so

Answer 38

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

Answer 39

@satellite73

Answer 40

I have no clue how to find the second answer

Answer 41

@dan815

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

so maybe we multiply the results to get 5,280*1,296 = 6,842,880

that result seems way too big though

Answer 47

it is because its bigger than the total number of ways

Answer 48

good point

Answer 49

I found it :D 216/715

Answer 50

I'm curious as to how you got that

Answer 51

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