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COUNT ON ME SINGAPORE Sum of the things that make us Singaporean

OPEN SESAME

Singaporeans are known to be extra hardworking – do you know that in 2016, we clocked one of the longest working hours in the world?

Not surprisingly, Singaporean Alan goes back to work on a Saturday and gets stuck outside his office because he has forgotten his new 4-digit keycode. He remembers the 4 digits, which are all different, but not their sequence. What are the chances of him getting in on his first try?

Solution

To find out the chances of him getting in, we need to know how many different sequences the numbers can come in – in other words, how many different permutations of the code there are.

Definition of Permutation:
A permutation is a possible way in which a set of objects can be arranged.

Permutation

The number of permutations of n distinct objects is given by n!

For example, the number of permutations of 5 distinct objects is 5!, where

5! = 5 x 4 x 3 x 2 x 1

(that is, multiply all positive whole numbers less than or equal to 5).

In this case, because Alan remembers the 4 digits, we only need to find out how many different permutations of these 4 digits there are. Hence, n = 4.

So the number of permutations
4!= 4 x 3 x 2 x 1
= 24

There are 24 possible permutations to the keycode.

So the chances of Alan unlocking the door on his first try is
124 ≈ 0.04

That’s only a 4% chance of succeeding on his first try.