Question

Suppose you need to choose a new combination for your combination lock. You have to choose 3 numbers, each different and between 0 and 40. How many combinations are there? Explain

Answer 1

Answer:

63,960 possibilities in total.

Step-by-step explanation:

For the first number, you can choose from 41 different numbers, so there are 41 possibilities.

For the second number, you cannot choose the same as the first one, so you are now limited to 40 possibilities.

For the third number, you are down to 39 possibilities since you cannot pick the same as the first two ones.

So, you have 41 * 40 * 39 = 63,960 possibilities in total.

Picking a new combination is easy... remembering it is the hard part :-)

If you want to calculate it from a formula standpoint, the base formula would be:

$P(n,r) = \frac{n!}{(n-r)!} = \frac{41!}{(41-3)!} = 63960$

Where n is the total numbers possible and r is the quantity of numbers you have to pick.