Q.

The students S1,S2,...,S10 are to be divided into 3 group 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_____________

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answer is 39449.

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Detailed Solution

=C3   1027-2+C4   1026-2+…..+C10   10=∑r=310Cr   10210-r-2∑r=310Cr   10=(1+2)10-C0   10210+C1   1029+C2   1028-2210-C0   10+C4   10+C2   10=39449
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The students S1,S2,...,S10 are to be divided into 3 group 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_____________