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In how many ways can (7) distinct books be arranged on a shelf so that two particular books are neither together nor both at the ends?(7) अलग-अलग पुस्तकों को शेल्फ पर कितने तरीकों से रखा जाए ताकि दो विशेष पुस्तकें न तो साथ हों और न ही दोनों सिरों पर हों?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (3720)(3720)
Subtract together cases (6!\cdot2!) and both-end cases (2!\cdot5!) from (7!). There is no overlap because both-end positions are not together, so the result is (5040-1440-240=3360).कुल (7!) से साथ वाली (6!\cdot2!) और दोनों सिरों वाली (2!\cdot5!) व्यवस्थाएं घटाएं। overlap साथ नहीं हो सकता, इसलिए (5040-1440-240=3360) मिलता है।
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