Question

Timothy is re-arranging his marble collection. He has five identical blue marbles,
five identical green marbles and three identical black marbles. He can fit exactly five
marbles into a case and must have at least one of each. How many different ways
can he arrange the case in​

Answer 1

Step-by-step explanation:

Given Timothy is re-arranging his marble collection. He has five identical blue marbles, five identical green marbles and three identical black marbles. He can fit exactly five marbles into a case and must have at least one of each. How many different ways can he arrange the case in

• Timothy has 5 blue, 5 green and 3 black marbles. We need to find the different ways of arranging five marbles that exactly fit in the case.
• Timothy has two ways to fit the marbles.
• So taking 2 each of 2 types and one of the third type we get that is 3 ways to pick and so 1 marble is to be taken.
• Ways to arrange will be
•                             5! / 2! x 2!
•                              120 / 4
•                                = 30
•        So total will be 30 x 3 = 90
• Also consider 3 of one type and one each of other types.
• So 3 ways to pick the type for which 3 marbles are to be taken and the ways to arrange will be 5! / 3!
•     = 120 / 6
•     = 20
• So total will be 20 x 3 = 60
• Therefore the number of ways to arrange will be 90 + 60 = 150

Reference link will be

https://brainly.in/question/26849366