## ssgayle 2 years ago Night engineers are going on an energy assessment in 3 cars that hold 2, 3, and 4 passengers, respectively. In how many ways is it possible to transport the 9 engineers to the manufacturing facility, using all cars?

1. ssgayle

what?

2. rushal

9C3 = . 9! ------- = 6! 3! 9 x 8 x 7 ------------- = 84 <==ANSWER 3 x 2 x 1 I hope that helps!! :-)

3. ssgayle

okay thats what i thought can you help me with one other problems?

4. rushal

sure if i can figure it out

5. ssgayle

A construction company employs two sales engineers, John and Meghan. John does the work of estimating cost for 70% of the jobs bid by the company. Meghan does the work for 30% of the jobs bid by the company. It is known that the error rate for John is such that 0.02 is the probability of an error when he does the work, whereas the probability of an error in the work of Meghan is 0.04. Suppose the bid arrives and a serious error occurs in estimating cost. Which engineer would you guess did the work? Explain and show work.

6. ssgayle

if u can that would be great!

7. satellite73

why is it $$\binom{9}{3}$$ ?

8. rushal

@satellite73 what bro ?

9. satellite73

pretty sure that is not right

10. rushal

i guess but i m just trying to help -_-

11. satellite73

you have $$9$$ people to order in groups of 2, 3, and 4 i am fairly sure that the number of ways to do this is $\frac{9!}{2!3!4!}$

12. satellite73

hey no problem, i just don't think "9 choose 3" is the right way to solve it

13. satellite73

you have $$9!$$ ways to order the people then divide by the number of ways to permute the people in each car

14. satellite73

also notice that the "9 choose 3" approach ignores completely the number of people in each car

15. ssgayle

ooooo i see cause it has to be either 2 groups or 3 or 4... if it was just random groups then it could be 9 chose 3?

16. rushal

i got it too satellite73 is correct my bad -_-

17. satellite73

9 choose 3 has really nothing to do with this problem it is the way to choose 3 things from a set of 9

18. satellite73

it all comes from the counting principle |dw:1378173059624:dw|

19. ssgayle

would you be able to help me with another difficult problem satellite or rushal? A construction company employs two sales engineers, John and Meghan. John does the work of estimating cost for 70% of the jobs bid by the company. Meghan does the work for 30% of the jobs bid by the company. It is known that the error rate for John is such that 0.02 is the probability of an error when he does the work, whereas the probability of an error in the work of Meghan is 0.04. Suppose the bid arrives and a serious error occurs in estimating cost. Which engineer would you guess did the work? Explain and show work.

20. satellite73

this is probably easiest if you do it with numbers lets imagine there are 1000 jobs total

21. satellite73

700 are done by john, 300 by meghan

22. satellite73

$$.02\times 700=14$$ mistakes are made by john and $$.04\times 300=12$$ by meghan

23. satellite73

so it is pretty damned close, but john makes more mistakes

24. ssgayle

yea i wasnt quite sure what to do with the numbers but that makes sense since its a rate in in units work/ mistake

25. ssgayle

can we do one more proeblem... sorry i keep asking but these few have been bothering me