There are 3 states and 3 students representing each state. In how many ways can 5 students be chosen such that at Least one student is chosen from each state.
Pick one:  A) 108.  B) 118  C) 128  D) 138  E) 148
To choose 5 students so that atleast one student will represent each state can be done in two ways:   A. 3-1-1 (3 students from 1 state and 1 student from other two states)   3C1*3C3*3C1*3C1=27   3C1 - # of ways to choose 3-student state;   3C3 - # of ways to choose 3 students from 3-student state;   3C1 - # of ways to choose 1 student from the first 1-student state;   3C1 - # of ways to choose 1 student from the second 1-student state.   OR   B. 1-2-2 (1 student from 1 state and 2 students from other two states)   3C1*3C1*3C2*3C2=81   3C1 - # of ways to choose 1-student state;   3C1 - # of ways to choose 1 student from the 1-student state;   3C2 - # of ways to choose 2 students from the first 2-student state;   3C2 - # of ways to choose 2 students from the second 2-student state.   27+81= 
<gadget id="calculator">27+81</gadget>
<output>108</output>
108.   108.nswer: 108 108.
<result>A</result>
There are 3 states and 3 students representing each state. In how many ways can 5 students be chosen such that at Least one student is chosen from each state.