Multiple choice

In how many different ways can the letters of the word ‘EUROPEAN’ be arranged so that R and N never come together ? शब्द ‘EUROPEAN’ के अक्षरों को कितने तरीके से व्यवस्थित कर सकते हैं कि R और N एकसाथ न आयें ?

  1. 10080

  2. 40320

  3. 35280

  4. 5040

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Total arrangements of EUROPEAN (8 letters with E repeated twice) = 8!/2! = 20160. Arrangements where R and N ARE together: treat RN or NR as one unit, giving 7 units with E repeated twice = 7!/2! × 2 = 5040. Therefore, arrangements where R and N NEVER come together = 20160 - 5040 = 15120. Option A (10080) incorrectly counts only the together cases.

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