1.

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 is1). 44/1202). 1/1203). 1/54). Cannot be determined

Answer»

? 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

5C1 × [4! - 4C1 × {3! – (3C1 × 1 + 1)} + 4C2 × 1 + 1] + 5C2 × {3! – (3C1 × 1 + 1)} + 5C3 × 1 + 1

? No. of Favorable Outcomes = Total Outcomes - Unfavorable Outcomes

= 120 - [5 × 9 + 10 × 2 + 10 + 1]

= 120 - 45 - 20 - 11 = 44

⇒ Probability = 44/120


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