Question

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?______

Answer 1

much easier than the last one

Answer 2

Similar to the other one right?

Answer 3

\[\dbinom{3}{2}\times \dbinom{6}{2}\times \dbinom{14}{3}\]

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

maybe you have seen it this way instead
\[3C2\]?

Answer 8

yes

Answer 9

3x2x1
-----
2x1
?

Answer 10

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
\[\frac{6\times 5}{2}=15\]

Answer 11

how do u get the 6 and 5

Answer 12

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)

Answer 13

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

Answer 14

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

Answer 15

so there are only two then correct?

Answer 16

two what?

Answer 17

are there two cases for this

Answer 18

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

Answer 19

wow you are a genius
16380

Answer 20

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

Answer 21

got disconnected