Question 1209238
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It is instructional to the student to see that the three groups can be formed in any order.<br>
(1) Choose the "group" of 1 student first<br>
Choose the 1 student from among the 7 in C(7,1) = 7 ways
Choose either group of 3 students from among the remaining 6 students in C(6,3) = 20 ways
Choose the last group of 3 students from among the remaining 3 students in C(3,3) = 1 way<br>
Total number of ways: 7*20*1 = 140<br>
(2) Choose the "group" of 1 student second<br>
Choose 3 students from among the 7 in C(7,3) = 35 ways
Choose the "group" of 1 student from among the remaining 4 students in C(4,1) = 4 ways
Choose the last group of 3 students from among the remaining 3 students in C(3,3) = 1 way<br>
Total number of ways: 35*4*1 = 140<br>
(3) Choose the "group" of 1 student last<br>
Choose 3 students from among the 7 in C(7,3) = 35 ways
Choose the second group of 3 students from among the remaining 4 students in C(4,3) = 4 ways
Choose the last "group" of 1 student from among the remaining 1 student in C(1,1) = 1 way<br>
Total number of ways: 35*4*1 = 140<br>