RRB NTPC CBT-1 practice question
A 4-character code is formed using 4 available symbols P, Q, R, S (repetition allowed), such that the code either starts with P or ends with P (or both). How many such codes are possible?
From a RRB NTPC CBT-1 Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (B) 112
Codes starting with P: 1 × 4 × 4 × 4 = 64. Codes ending with P: 4 × 4 × 4 × 1 = 64. Codes both starting and ending with P: 1 × 4 × 4 × 1 = 16. By inclusion-exclusion, codes starting with P or ending with P = 64 + 64 − 16 = 112.
हिंदी में प्रश्न
4 उपलब्ध प्रतीकों P, Q, R, S (पुनरावृत्ति की अनुमति) का उपयोग करके एक 4-वर्ण कोड इस प्रकार बनाया जाता है कि कोड या तो P से शुरू हो या P पर समाप्त हो (या दोनों)। ऐसे कितने कोड संभव हैं?
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सही उत्तर: (B) 112
P से शुरू होने वाले कोड: 1 × 4 × 4 × 4 = 64। P पर समाप्त होने वाले कोड: 4 × 4 × 4 × 1 = 64। P से शुरू और P पर समाप्त दोनों वाले कोड: 1 × 4 × 4 × 1 = 16। समावेशन-अपवर्जन सिद्धांत से, P से शुरू या P पर समाप्त होने वाले कोड = 64 + 64 − 16 = 112।
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