The number lock of a suitcase has 4 wheels, ...

NCERT Class XI Mathematics - Probability - Solutions

Question : 55 of 54

Marks: +1, -0

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 =

\frac{1}{5040}

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