The students S1, S2, ....., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is ___________.
Answer (integer)
31650
Solution
If group C has one student then number of
groups
<br><br>= <sup>10</sup>C<sub>1</sub>
[2<sup>9</sup>
– 2] = 5100
<br><br>If group C has two students then number of
groups
<br><br>= <sup>10</sup>C<sub>2</sub>
[2<sup>8</sup>
– 2] = 11430
<br><br>If group C has three students then number of
groups
<br><br>= <sup>10</sup>C<sub>3</sub>
× [2<sup>7</sup>
– 2] = 15120
<br><br>So total groups = 31650
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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