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Permutation & Combination is a method of counting the number of ways of selection and arrangement. In GMAT, the problems related to this topic can be straight forward or they can be complex where you have to make cases. Let us look at some of the questions from this topic:
1. At a meeting of 7 joint chiefs of staff, the chief of air staff does not want to sit next to the chief of the army. How many ways can the seven chiefs of staff be seated around a circular table?
Evidently, it is a question of circular permutation. We know that the number of ways to arrange n items in a circular arrangement is (n-1)!
Thus, the number of ways in which 7 people can be arranged around a circular table is
                                              (7-1)! = 6!                                             (1)
Number of ways in which 7 people can be arranged keeping the air and army chiefs together is
                                                     5! * 2!                                               (2)
Therefore, the number of ways in which 7 people can be arranged such that the 2 chiefs never be together is
                                              6! – 5! * 2! = 5!(6-2) = 480
2. A family consisting of one mother, one father, two daughters and a son is taking a road trip in TATA Nano. The Nano has two front seats and three rear. One of the parents has to drive, and two daughters refused to sit next to each other. Find the number of ways in which the seating can be done.
The driver seat can be filled by 2 people- the mother or the father.
The front seat can be taken by one of the daughters. Or both the daughters can sit in the rear. So, there are 2 possibilities here:
1. If one of the daughters is sits in the front seat beside the driver, the front seat can be filled in 2 ways, and the rear seats can be arranged with 3!
Therefore , total no. of possibilities = 2*2*3!= 24
2. If both the daughters are seated in the rear, we know that none of the daughters can take the middle seat. Therefore they have to sit at the rear window seats, which can be arranged in 2! ways. Rest of the people will be arranged by 2!. Hence total possibilities for this case is 2 *2! *2! = 8
Therefore the total number of the seating arrangements possible is 24 + 8 = 32.
Also Read: How to Write Essays in GMAT AWA?
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