In How Many Ways Can 3 Grade School Students, 2 Junior High School Students, And 4 Senior High School Students Be Seated In A Long Straight Desk If Th

In how many ways can 3 grade school students, 2 junior high school students, and 4 senior high school students be seated in a long straight desk if the student of the same level are each to sit together?

A. 38
B. 72
C. 288
D. 1728

 

1728 ways

Computation:

The following represent,

factorial 3 = arrangement of 3 grade school students

factorial 2 = arrangement of 2 junior high school students

factorial 4 = arrangement of 4 senior high school students

factorial 3 = arrangement of students by school level

By fundamental counting principle,

3!\times2!\times4!\times3!\\\\\left\begin{array}{ccccc}3!&=&3\times2\times1&=&6\\2!&=&2\times1&=&2\\4!&=&4\times3\times2\times1&=&24\\3!&=&3\times2\times1&=&6\end{array}\right\\\\6\times2\times24\times6\\\\=\boxed{1728\:ways}


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