Answer:
a) 1,440 ways
b) 59,280 or 64,000
Explanation:
a) Aircraft boarding.
8 people, 2 in first class, boarding first, then 8 economy class.
The 2 people in first class board first, but they can board as AB or BA... so 2 ways here.
For the 6 economy class passengers, we have a permutation of 6 out of 6, so 720, as follows:
Since the two are independent, we multiply them to have a global number of ways: 2 * 720 = 1,440 different ways for the 8 passengers to board that plane.
b) combination lock.
Here we do have a little problem... the question doesn't specify if the 3 numbers are different numbers of not. So, we'll calculate both:
Numbers go from 1 to 40 inclusively... so 40 possibilities.
Normally, in a combination lock, the numbers are different, so let's start with that one:
First number: 40 options available
Second number: 39 options available (cannot take the first one again)
Third number: 38 different options (can't take First or Second number again)
Overall, we then have 40 * 39 * 38 = 59,280 different lock combinations.
If we can pick pick the same number twice:
First number: 40 options available
Second number: 40 options available
Third number: 40 options available
Overall 40 * 40 * 40 = 64,000 different lock combinations