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Misc 10 - Number lock of a suitcase has 4 wheels, each - Using permutation

Misc 10 - Chapter 16 Class 11 Probability - Part 2


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Misc 10 The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase? There are 10 digits out of which 4 digits to be chosen with no repeats Hence , n(S) = Total 4 digit numbers out 10 digits = 10P4 = 10!﷮ 10 −4﷯!﷯ = 10!﷮6!﷯ = 10 × 9 × 8 × 7 × 6!﷮6!﷯ = 5040 Let A be the event that correct sequence is selected There can be only 1 correct sequence Hence n(A) = 1 P(A) = n(A)﷮n(S)﷯ = 𝟏﷮𝟓𝟎𝟒𝟎﷯

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.