Ashish has 27 red marbles and 45 green marbles. He wants to arrange them in equal rows. He also wants each row have only one colour of marble. What are the different ways that he can do this? (Show method with statements)
Answers
Given : Ashish has 27 red marbles and 45 green marbles.
Arrange them in equal rows.
Each row have only one colour of marble.
To Find : different ways that he can arrange marbles
Solution:
To arrange in Equal rows need to have common Divisors
Factors of 27 = 1 , 3 , 9 , 27
Factors of 45 = 1 , 3 , 5 , 9 , 15 , 45
Common Divisors 1 , 3 , 9
Each row has 9 marbles
27/9 = 3 , 45/9 = 5
Then 3 Rows of Red and 5 Rows of Green
Total Rows = 8
Can be arranged in 8!/(5!.3!) ways = 56 ways
Each row has 3 marbles
27/3 = 9 , 45/3 = 15
Then 9 Rows of Red and 15 Rows of Green
Total Rows = 24
Can be arranged in 24!/(15!.9!) ways = 13,07,504 ways
If Each row has 1 marbles
Then similarly 72!/(27!.45!) ways
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Step-by-step explanation:
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