Question

Q3) Bruce and Krista are going to buy a new furniture set for their living room. They want to buy a couch, a coffee table, and a recliner. They have narrowed it down so that they are choosing between 4 couches, 5 coffee tables, and 9 recliners. How many different furniture combinations are possible? *

Answer 1

Step-by-step explanation:

Given Q3) Bruce and Krista are going to buy a new furniture set for their living room. They want to buy a couch, a coffee table, and a recliner. They have narrowed it down so that they are choosing between 4 couches, 5 coffee tables, and 9 recliners. How many different furniture combinations are possible? *

• According to the question  
• Total number of couches they choose will be 4
• Total number of coffee tables they choose will be 5
• Total number of recliners they choose will be 9
• So they need to buy 1 couch, 1 coffee table and 1 recliner.
• So combination of couches will be 4 C1 = 4!  / (4 – 1)!
•                 = 4! / 3!
•    =  4
• Combination of coffee tables will be 5 C1 = 5! / (5 – 1)!
•     = 5! / 4!
•    = 5
• Also combination of recliner will be 9 C1 = 9! / (9 – 1)!
•    = 9! / 8!
•    = 9
• So total combination will be 4 x 5 x 9 = 180 ways

Reference link will be

https://brainly.in/question/2299026