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THERE ARE 10 PRIZES AND 4 STUDENTS. WE WANT ONLY TWO STUDENTS TO GET THE PRIZES. HOW MANY WAYS ARE THERE??
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Here's a simple approach:

Ways of selecting pair of 2 students=  4C=  6

Ways of distributing 10 prizes among 2 students= 210 = 1024

Total ways till now = 6 * 1024  = 6144 but there are cases that we want to remove like student A getting all the 10 prizes. As A appears in 3 pairs i.e (A,B), (A,C), (A,D). Hence 3 cases for student A. Total such cases for 4 students = 3 * 4= 12

Hence 6144 - 12 = 6132 ways

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