hemant_rajput wrote:Another approach -
First fix A.
Now total possible arrangement - 5! = 120
Arrangements when D and F sit next to = make D and F sit next to A * the rest of available seats with rest of the members = 2! * 3! = 12
120 - 12 = 108
Answer c
You have correctly subtracted from the total Bad Case 1: the arrangements in which BOTH D AND F sit next to A.
But we must also subtract from the total Bad Case 2: the arrangements in which EITHER D OR F -- but NOT both -- sit next to A.
Bad Case 2: Either D or F (but not both) next to A
Number of options for the disallowed person sitting next to A = 2. (Either D or F.)
Number of seat options for the disallowed person = 2. (To the right or left of A.)
Number of options for the OTHER seat next to A = 3. (Anyone but D or F, since only one of them can sit next to A.)
Number of ways to arrange the remaining 3 people = 3!.
To combine these options, we multiply:
2*2*3*3! = 72.
Thus:
Total favorable arrangements = total possible arrangements - bad case 1 - bad case 2 = 120-12-72 = 36.
Last edited by
GMATGuruNY on Mon Aug 12, 2013 7:37 am, edited 1 time in total.
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