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In arrangements of the letters of (TRIANGLE), how many have (T) not first and (E) not last?शब्द (TRIANGLE) के अक्षरों की व्यवस्थाओं में (T) पहले और (E) अंतिम न हो, ऐसी व्यवस्थाओं की संख्या कितनी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (30960)(30960)
Use inclusion-exclusion on total (8!), subtracting cases with (T) first and (E) last: (8!-7!-7!+6!). Exam tip: add back the overlap in two forbidden conditions.कुल (8!) से (T) first और (E) last वाले मामलों को inclusion-exclusion से घटाएं, यानी (8!-7!-7!+6!)। परीक्षा में दो निषेध शर्तों में overlap जोड़ना न भूलें।
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