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Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.

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Ten students are to be selected for a project from a class of 30 students.

Case I:

If 4 students join the project, then from remaining 26 students, rest of the 6 students are to be selected

Which can be done in 26C6

= 230230 ways

Case II:

If 4 students does not join the project, then from remaining 26 students, all the 10 students are to be selected.

Which can be done in 26C10

= 5311735 ways.

∴ Required number of selections = 26C6 + 26C10

 = 230230 + 5311735

 = 5541965

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