Honored students

Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them?

Correct result:

n =  12870


C3(13)=(133)=13!3!(133)!=131211321=286 C2(10)=(102)=10!2!(102)!=10921=45  n=(102) (251023)=45 (251023)=12870

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