See, Let there be a case in which the three design books are on one side of the shelf covering three out of nine places. Now, the ways to arrange those three design books is 3! = 6 and the number of ways to arrange the rest of the mathematics books is 6!. So total ways are 6! x 3! = 4320.
But the set of three design books can be moved to different 3 places instead of the first three. So total ways are
7 x 4320= 30240.

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TopNewestSee, Let there be a case in which the three design books are on one side of the shelf covering three out of nine places. Now, the ways to arrange those three design books is 3! = 6 and the number of ways to arrange the rest of the mathematics books is 6!. So total ways are 6! x 3! = 4320. But the set of three design books can be moved to different 3 places instead of the first three. So total ways are 7 x 4320= 30240.

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