NCERT Class XI Mathematics - Probability - Solutions
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Question : 55
Total: 54
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?
Solution:
There are total 10 digits from 0 to 9.
Since the digits cannot be repeated, so the first place may be filled in 10 ways, second place in 9 ways, third place in 8 ways and fourth place in 7 ways.
∴ Number of possible outcomes = 10 × 9 × 8 × 7 = 5040
The lock of suitcase can be opened in 1 way only.
∴ Number of favourable cases = 1
Thus, required probability =
Since the digits cannot be repeated, so the first place may be filled in 10 ways, second place in 9 ways, third place in 8 ways and fourth place in 7 ways.
∴ Number of possible outcomes = 10 × 9 × 8 × 7 = 5040
The lock of suitcase can be opened in 1 way only.
∴ Number of favourable cases = 1
Thus, required probability =
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