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In how many ways can (5) distinct red balls and (4) distinct blue balls be arranged in a row so that no two blue balls are together?(5) अलग-अलग लाल और (4) अलग-अलग नीली गेंदों को ऐसे पंक्ति में रखें कि कोई दो नीली गेंदें साथ न हों। तरीकों की संख्या क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (86400)(86400)
Arrange the red balls first in (5!) ways, then place (4) blue balls in (6) gaps in (^{6}P_4) ways. The total is (5!\cdot^{6}P_4=86400).पहले लाल गेंदें (5!) तरीकों से रखें, फिर (6) gaps में (4) नीली गेंदें (^{6}P_4) तरीकों से रखें। कुल (5!\cdot^{6}P_4=86400) है।
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