A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour ?
The correct answer is (C) 24.
Explanation:
A flag has 4 horizontal stripes to be designed using some or all of the colours red, green, and yellow (3 available colours), such that no two adjacent stripes have the same colour. Let the 4 stripes be S1, S2, S3, and S4 from top to bottom. For the first stripe S1, we can choose any of the 3 available colours (3 choices). For the second stripe S2, it must be different from S1, so we have 2 choices remaining. For the third stripe S3, it must be different from S2, so we have 2 choices remaining (it can be the same as S1, as long as it differs from S2). For the fourth stripe S4, it must be different from S3, so we have 2 choices remaining. Total number of different ways = 3 × 2 × 2 × 2 = 24 ways. Therefore, option (c) is correct.
हिंदी में प्रश्न एवं आदर्श उत्तर
किसी ध्वज को लाल, हरे या पीले रंगों में से कुछ या सभी रंगों का उपयोग कर चार क्षैतिज पट्टियों द्वारा परिरूपित करना है। कितने ऐसे विभिन्न तरीकों से इसे किया जा सकता है, इस प्रकार कि कोई भी दो आसन्न पट्टियाँ एक ही रंग की न हों ?
सही उत्तर (C) 24 है।
व्याख्या:
A flag has 4 horizontal stripes to be designed using some or all of the colours red, green, and yellow (3 available colours), such that no two adjacent stripes have the same colour. Let the 4 stripes be S1, S2, S3, and S4 from top to bottom. For the first stripe S1, we can choose any of the 3 available colours (3 choices). For the second stripe S2, it must be different from S1, so we have 2 choices remaining. For the third stripe S3, it must be different from S2, so we have 2 choices remaining (it can be the same as S1, as long as it differs from S2). For the fourth stripe S4, it must be different from S3, so we have 2 choices remaining. Total number of different ways = 3 × 2 × 2 × 2 = 24 ways. Therefore, option (c) is correct.