Q: 4 (IAS/2003)
question_subject:
Logic/Reasoning
question_exam:
IAS
stats:
0,2,6,2,3,2,1
keywords:
{'flags': [0, 0, 1, 0], 'single flag': [0, 0, 1, 0], 'different codes': [0, 0, 1, 0], 'different colours': [0, 0, 2, 0], 'colours': [0, 2, 4, 9], 'different colour': [0, 1, 1, 0], 'maximum number': [1, 0, 1, 2], 'colour': [11, 6, 13, 28], 'military exercise': [0, 0, 2, 3], 'different sequence': [0, 0, 1, 0]}
In this question, we are asked to determine the maximum number of codes that can be generated using three differently colored flags in various sequences.
(i) Single flag of different colours: This can generate three different codes, one for each color.
(ii) Any two flags in a different sequence of colours: You can choose 2 flags out of 3 in 3 ways. And each pair of flags can be arranged in 2 different ways. So this can generate 3*2 = 6 different codes.
(iii) Three flags in a different sequence of colour: This can be arranged in 3 factorial = 6 ways.
If you add up all of these, you get the total number of possible codes, which is 3 (from the single flag) + 6 (from the two flags) + 6 (from the three flags) = 15.
So, option 3 (15) is correct.