In general, the number of ways of arranging n objects around a round table is (n-1)! An easier way of thinking is that we "fix" the position of a particular person at the table. Then the remaining n -1 persons can be seated in (n-1)! ways. Done! Thus the number of ways of arranging n persons along a round table so that no person has the same two neighbours is(n-1)!/2 Similarly in forming a necklace or a garland there is no distinction between a clockwise and anti clockwise direction because we can simply turn it over so that clockwise becomes anti clockwise and vice versa. Hence the number of necklaces formed with n beads of different colours = (n-1)!/2 Illustrative ExamplesExampleIn how many ways can 3 men and 3 women be seated at a round table if
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Answers1. (i) 240 (ii) 480 2. 576 3. 604. (i) 60 (ii) 1 5. 2880 6. 3628800 7. 86400 8. 4 9. (i) 2(18!) (ii) 17(18!) (iii) 2(18!) 10. 80640 11. (i) 2 (ii) 2 12. 4 No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! Open in App Suggest Corrections |