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Restrictions and Exceptions in Combination
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Methods for solving problems with restriction and Mississippi rule for identical items

Srijita Banerjee
B.Tech in Biotechnology\singer\loves teaching\public speaker\peer educator\Bengali

U
what strategy to follow for particular , rules ? while doing this. how to do??
1. COMBINATROICS: FUNDAMENTALS GRE QUANTS SRIJITA BANERJEE https://unacademy.com/user/mampi

2. Restrictions Test won't give you arrange five girls in order Rather it would be given: 1st girl sitting next to 2nd /x girl sitting next to z 02

4. Let us consider 5 students: A,B,C,D and E. In how many ways can you seat them if D needs to be in the middle and B always needs to be beside D? 02

5. Let us consider 5 students: A,B,C,D and E. In how many ways can you seat them if D needs to be in the middle and B always needs to be beside D? 1*2*3 02

6. Let us consider 5 students: A,B,C,D and E. In how many ways can you seat them if D needs to be in the middle and B always needs to be beside D? 02

7. Let us consider 5 students: A,B,C,D and E. In how many ways can you seat them if D needs to be in the middle and B always needs to be beside D? 02

8. Let us consider 5 students: A,B,C,D and E. In how many ways can you seat them if D needs to be in the middle and B always needs to be beside D? 02

9. Let us consider 5 students: A,B,C,D and E. In how many ways can you seat them if D needs to be in the middle and B always needs to be beside D? 1*2*3 02

10. Let us consider 5 students: A,B,C,D and E. In how many ways can you seat them if D needs to be in the middle and B always needs to be beside D? 1*2*3*2 02

11. Simple Equation n!total number of stages or arrangements .RNumber that obeys the restriction QNumber that does not obey the restriction Thus, n! R+Q 02

12. Five students: A, B, C, D and E are to be arranged in a line. How many such arrangements are possible if B is not allowed to stand next to D? B can only stand beside D B and D becomes one unit B D----DB-- Thus, 2(4 3 2*1) = 48 02

13. IDENTICAL ITEMS Another type

14. A librarian has got 8 books, 5 of them are novels and 3 of them are identical copies of the same dictionary. In how many different ways can they be arranged? 02

15. A librarian has got 8 books, 5 of them are novels and 3 of them are identical copies of the same dictionary. In how many different ways can they be arranged? . Considering seven different books, the factorial is 8! But if we look into it closely, the dictionaries are the same/ identical so the different arrangements would ultimately give same results. EFGHID1 D2 D3 D1 EFGD2 D3 H I Dictionaries alone: 3! 02