# 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:**

The number lock has 4 wheels, each labelled with digits from 0 to 9.

Number of ways of selecting 4 different digits out of 10 digits = ¹⁰C₄ (Using combinations).

Now, each combination of 4 different digits can be arranged in (4)! ways.

Hence the number sequence of four digits with no repetitions = ¹⁰C₄ × (4)!

¹⁰C₄ × (4)! = [(10)!/(4)!(10 - 4)!] × (4)!

= [10! / 4! 6!] × (4)!

= 5040

There is only one number that can open the suitcase.

Thus, the required probability is 1/5040

NCERT Solutions Class 11 Maths Chapter 16 Exercise ME Question 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?

**Summary:**

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. The probability of a person getting the right sequence to open the suitcase is 1/5040