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An S5 math probid questions

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1. 8 Students A-H and 2 teachers line up to take a photograph. How many different possible arrangements are there if: a: teachers are in middle b: students A&B have to be separated c: teachers in middle and A&B have to be separated?

最佳解答:

(a) SSSSTTSSSS teachers are in middle, 2P2 ways A-H are in the rest, 8P8 ways thus the required no. of arrangements = 2P2 x 8P8 = 80640 (b) _T_T_C_D_E_F_G_H_ arrange teachers and C,D,E,F,G,H, 8P8 ways A and B in the spaces ”_”, 9P2 ways thus the required no. of arrangements = 8P8 x 9P2 = 2903040 (c) case(i)_S_S_S_TT_S_S_S_ teachers are in middle, 2P2 ways arrange C,D,E,F,G,H, 6P6 ways A in left four spaces and B in right four spaces, 4P1 x 4P1 ways case(ii)_S_S_S_TT_S_S_S_ teachers are in middle, 2P2 ways arrange C,D,E,F,G,H, 6P6 ways A in right four spaces and B in left four spaces, 4P1 x 4P1 ways case(iii)_S_S_TTSSSS teachers are in middle, 2P2 ways arrange C,D,E,F,G,H, 6P6 ways A and B in the spaces, 3P2 ways case(iv)SSSSTT_S_S_ teachers are in middle, 2P2 ways arrange C,D,E,F,G,H, 6P6 ways A and B in the spaces, 3P2 ways thus the required no. of arrangements = (2P2 x 6P6 x 4P1 x 4P1) x 2 + (2P2 x 6P6 x 3P2) x 2 = 63360

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