Subject
Quantitative Aptitude
Topic
Probability
Five letters are sent to different persons and addresses on the five envelopes are written ।at random. The probability that all the letters do not reach the correct destiny is
Five letters are sent to different persons and addresses on the five envelopes are written ।at random. The probability that all the letters do not reach the correct destiny is
ক)
44/120খ)
1/120গ)
1/5ঘ)
Cannot be determinedঙ)
None of theseExplanation
∵ Probability = [No of Favorable Outcomes/No. of Total Outcomes] ⇒ No. of Total Outcomes = Total No. of ways in which 5 envelopes can be sent to 5 persons = 5! = 120 No. of Favorable Outcomes = when none of the letters reaches correct destiny Unfavorable cases = when all the five envelope reaches to their destiny + when one of them reaches to its correct destiny + two of them reaches to its correct destiny + three of them reaches their correct place 5 C 1 × [4! - 4 C 1 × {3! – ( 3 C 1 × 1 + 1)} + 4 C 2 × 1 + 1] + 5 C 2 × {3! – ( 3 C 1 × 1 + 1)} + 5 C 3 × 1 + 1 ∵ No. of Favorable Outcomes = Total Outcomes - Unfavorable Outcomes = 120 - [5 × 9 + 10 × 2 + 10 + 1] = 120 - 45 - 20 - 11 = 44 ⇒ Probability = 44 / 120Related questions
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