Jennifer is setting the dinner table. She needs to set the table for 4 people, and each person needs to have an identical place setting to the other 3. She has 6 red place mats,6 green place mats, and 8 blue place mats as well as 4 maroon napkins, 3 orange napkins,5 beige napkins, and 8 purple napkins. How many different combinations of place mats and napkins could she have at any given place setting, if each place setting consists of exactly one place mat and one napkin?

Question

Jennifer is setting the dinner table. She needs to set the table for 4 people, and each person needs to have an identical place setting to the other 3. She has 6 red place mats,6 green place mats, and 8 blue place mats as well as 4 maroon napkins, 3 orange napkins,5 beige napkins, and 8 purple napkins. How many different combinations of place mats and napkins could she have at any given place setting, if each place setting consists of exactly one place mat and one napkin?

Answer 1

What a lot of extra verbiage to state the simple question:

How many place settings can I make from
3 kinds of place mats, and 3 kinds of napkins
(she can't use the orange ones, since she has only 3)

Since all the setting have to be the same, we just have to find one

number of different place setting = 3x3 or 9

Answer 2

a. 9

b. 12
c.102
d. 46,080
e. 138,240

Answer 3

To find the number of different combinations of place mats and napkins Jennifer could have at any given place setting, we need to multiply the number of options for each component.

Step 1: Calculate the number of options for the place mats:
Jennifer has 6 red place mats, 6 green place mats, and 8 blue place mats. Since each person needs an identical place setting, she can only choose one place mat for all four settings. Therefore, the number of options for the place mat is 6 (the total number of place mats).

Step 2: Calculate the number of options for the napkins:
Jennifer has 4 maroon napkins, 3 orange napkins, 5 beige napkins, and 8 purple napkins. Again, since each person needs an identical place setting, she can only choose one napkin for all four settings. Therefore, the number of options for the napkin is 4 (the total number of napkins).

Step 3: Find the total number of combinations:
To get the total number of combinations, we multiply the number of options for the place mats by the number of options for the napkins:
Number of combinations = Number of options for place mats * Number of options for napkins
= 6 * 4
= 24

Therefore, Jennifer could have 24 different combinations of place mats and napkins at any given place setting.