## anonymous 4 years ago A camper has 3 jackets, 6 sleeping bags, and 14 different packages of food. An outfit consists of 2 jackets, 2 sleeping bags, and 3 packets of food. How many ways can the trip be outfitted?______

1. anonymous

much easier than the last one

2. anonymous

Similar to the other one right?

3. anonymous

$\dbinom{3}{2}\times \dbinom{6}{2}\times \dbinom{14}{3}$

4. anonymous

is it clear how to compute these numbers, because in fact all i really did was restate the question in notation

5. anonymous

how exactly do i solve that notation? multiply? Cross multiply?

6. anonymous

sorry it has been forever since i had a math class now im in this finite course:)

7. anonymous

maybe you have seen it this way instead $3C2$?

8. anonymous

yes

9. anonymous

3x2x1 ----- 2x1 ?

10. anonymous

number of ways to choose 2 from a set of 3 is 3 number of ways to choose 2 from a set of 6 is $\frac{6\times 5}{2}=15$

11. anonymous

how do u get the 6 and 5

12. anonymous

yes that is one way to think about it. the other way is more basic. if you have three items and wish to select one, you pretty clearly have 3 choices. if you have three items and wish to select 2, you have the same three choice ( like selecting the one to exclude)

13. anonymous

you have 6 sleeping bags and wish to select 2 of them, six choices for first bag, 5 for second and you have to divide by two because order doesn't count

14. anonymous

the last one is therefore $\frac{14\times 13\times 12}{3\times 2}$

15. anonymous

so there are only two then correct?

16. anonymous

two what?

17. anonymous

are there two cases for this

18. anonymous

for this problem it is a straightforward multiplication $\dbinom{3}{2}\times \dbinom{6}{2}\times \dbinom{14}{3}$ $3\times 15\times 364$

19. anonymous

wow you are a genius 16380

20. anonymous

but....im not sure how you got 3x15x364 what do i do with the numbers inside ( ) exactly?

21. anonymous

got disconnected