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19 Sep 2023, 04:58
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
44% (02:50) correct
56%
(02:46)
wrong
based on 63
sessions
History
Date
Time
Result
Not Attempted Yet
A television channel has eight programs − A through H − which are available for three prime-time slots on a Sunday evening. In how many different ways can the programmes be shown, if, whenever both programs A and B are in the lineup, program A must come immediately after program B?
A. 228
B. 306
C. 312
D. 318
E. 336
A. 228
B. 306
C. 312
D. 318
E. 336
Choose 3 programs out of 8, 8C3 and arrange them in 3 slots - 3! so finally 8C3*3!=336
and based on the condition of A immediately after B so whenever A and B are chosen with other program, the cases not allowed are:
A x B, A B x, B x A, x A B : Here we have 6 choices for x. so total cases to exclude= 6*4 = 24
So finally 336 - 24 = 312
and based on the condition of A immediately after B so whenever A and B are chosen with other program, the cases not allowed are:
A x B, A B x, B x A, x A B : Here we have 6 choices for x. so total cases to exclude= 6*4 = 24
So finally 336 - 24 = 312
19 Sep 2023, 07:27
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Bunuel
Total Possibiliteis is 8P3
If, B occupies 1st place A occupies 2nd place and 3rd place can be occupied by 6 ways = 6 ways
If, B occupies 2nd place A occupies 3rd place and 1st place can be occupied by 6 ways = 6 ways
Now 8P3 includes B occupies 1st Place and B occupying 2nd place....
So, Possible ways is 8P3 - (6 + 6) = 336 - 24= 312, Answer IMHO must be (C)
