Question

(a) In how many ways can 7 people be lined up to get on a bus? (b) If 5 specific persons, among 7, insist on following each other, how many ways are possible? (c) If 2 specific persons, among 7, refuse to follow each other, how many ways are possible? (a) The 7 different people can be lined up in 5040 different ways. (b) The people can be lined up in different ways. (c) The people can be lined up in different ways.

Answer 1

(a) The 10 different people can be lined up in 1 - 10! dyferent ways = 3628800 ways. 6 24 4 specific persons are together, then 7 different people can be lined up in 71 ways. Again, the 4 specific persons can be arranged among them in 4! ways, Hence, the people can be lined up in 71x4! = 120960 ways. 24 2 specific persons are together, a dipperent people can be lined up in 9. & ays. Again, the 2 specific persons can be arranged among them in 2! ways. Thus, ich 2 specific persons are lagether, amang 10, the people can be lined up in 912! - 725,760 ways. Hence ich a specific persons are refused do follow each other, amang 10, the people can see lined up in (116! – 9.217 ways = 3628800- 725, 760 = 2903040 ways)