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A train goin from delhi to jaipur stops at 7 intermediate stations. 5 persons enter the train during the journey with 5 difefrent tickets of same class . How mant different set of tickets they could had??Solution) This is the condition if they all board the train from Delhi, though if they can board the train from any station . so here is the solutionEvery person can have two choices 1) Boarding Station 2)Destinationif B.S= Delhi Des=1,2,3,4,5,6,7,Jaipur = 8 choicesif B.S.= 1 Des=2,3,4,5,6,7,Jaipur = 7 choicesif B.S.= 2 Des=3,4,5,6,7,Jaipur = 6 choices...therefore the total type of tickets that a person can have =8+7+6+5+4+3+2+1 = 36choicesLikewise all the fove people can have these choices (May be recurring) .Then the total choices may be 365Though if they have different tickets then the permutation possible are 36*35*34*33*32
Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
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