10 distinct computational tasks are to be assigned to 3 processors. The first processor should receive 5 tasks, the second processor should receive 3 tasks, and the third processor should receive 2 tasks. The total number of different assignments that obey the given constraint is....

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is it 2520?, (10 choose 5) times (5choose3) times (2choose2)

\[3!\times (^{10}C_5\times ^5C_3\times ^2C_2)\]

why multiply by 3 factorial?

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