Given:
1 answer:
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(4/9)/(2/3)/(5/6)
First, invert and multiply. / Your problem should look like:
× 
Second, invert and multiply. / Your problem should look like:
× 
×
Third, apply this rule:
× 
. / Your problem should look like: 
Fourth, simplify 4 × 3 × 6 to 72. / Your problem should look like:
Fifth, simplify 9 × 2 × 5 to 90. / Your problem should look like:
Sixth, simplify. / Your problem should look like:
Original answer:
Answer as decimal: 0.8
First, invert and multiply. / Your problem should look like:
Second, invert and multiply. / Your problem should look like:
Third, apply this rule:
Fourth, simplify 4 × 3 × 6 to 72. / Your problem should look like:
Fifth, simplify 9 × 2 × 5 to 90. / Your problem should look like:
Sixth, simplify. / Your problem should look like:
Original answer:
Answer as decimal: 0.8
Answer:
a) 1,440 ways
b) 59,280 or 64,000
Step-by-step 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