Answer :
By using the concept of permutation, it can be calculated that
Number of ways in which the marbles of different sizes can be arranged in a line = 362880
What is permutation?
The technique which is used to determine the possible arrangements that can be made among the members of the set when the order of arrangement is taken into account
Here the concept of permutation is used
Number of red marbles = 2
Number of yellow marbles = 2
Number of green marbles = 5
Total number of marbles = 2 + 2 + 5 = 9
Here, the marbles are of different sizes
So the first marble have 9 choices, second marble have 8 choices and so on
Number of ways in which the marbles of different sizes can be arranged in a line = 9 [tex]\times[/tex] 8 [tex]\times[/tex] 7 [tex]\times[/tex] .... [tex]\times[/tex] 1
= 9!
= 362880
To learn more about permutation, refer to the link-
https://brainly.com/question/1216161
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