Question

having a VERY difficult time trying to solve combination/permutation problems? it's not clicking!?!??!

At the Peking Gardens restaurant, the menu features 5 items in column A, 6 in column B, 4 in column D, 8 in column E, and 5 in column F. For a NOBEL plate, you can order one item from each of columns A, B, C. How many different NOBEL plates are there? For an IMPERIAL plate, you can order two items from each of columns A, B and C or two each from columns D, E, and F. How many IMPERIAL plates can be ordered? How would I solve this?

Answer 1

this is fundamental theorem of counting

but you are missing the number in column C

A = 5
B = 6
C = ?
D = 4
E = 5
F = 8

Nobel plate = 5 x 6 x ?

just multiply the number of choices in each stage...

Answer 2

for the 2nd part the imperial

it uses combinations

column A selecting 2 from 5

which is

\[^5 C _{2} ~~or ~~\left(\begin{matrix}5 \\ 2\end{matrix}\right)\]

Answer 3

oh i understood the noble part, but im a bit confused for the imperial plate

Answer 4

if it's or, do i need to add the ABC and DEF columns together after multiplying?

Answer 5

how would i do it with only factorial? @campbell_st

Answer 6

again its multiplying

2 from A \[^5C_{2}\]

2 from B \[^6C_{2}\]

continue this the the solution is

\[^5C_{2} \times ~^6C_{2} \times .... \]