Professor Smith has to select 5 students out of his math classrandomly to partic

Question

Professor Smith has to select 5 students out of his math classrandomly to participate in a math contest. There are 36students in the class. (1) If 2 out of the 5 students selected will attend thenational contest, and the other 3 will go international, how manyways can Prof. Smith choose from his 36 students? Professor Smith has to select 5 students out of his math classrandomly to participate in a math contest. There are 36students in the class. (1) If 2 out of the 5 students selected will attend thenational contest, and the other 3 will go international, how manyways can Prof. Smith choose from his 36 students?

Explanation / Answer

You should use the binomial coeficient again, but you have toadd things... -- (36_C_5) will give you the number of ways to choose 5students. Once you have the five students chosen, you have to arrangethem... (5_C_2) will give you the number of ways to choose 2 studentsfrom the 5 to go to national. Then, the 3 remaining students, by default will go tointernational.
So, your answer will be the product of the two values... (36_C_5)*(5_C_2) = 3769920 -- Note... You could have also used (5_C_3) to arrange the fivestudents, but you should notice that 5C2 and 5C3 are exactly thesame.

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