In how many ways can 7 people line up for plane tickets?
In how many ways can 7 people line up for play tickets
At the head of the line, there are 7 choices of people.
The next one has six, then five, then four....
Since these are independent choices, the total number of ways are multiplied together to give
7*6*5*...1
=7!
find F26 the 26th term
If you want, you can start from
F0=0
F1=1
and from F2 and up, use
Fn=Fn-2+Fn-1 to continue:
F2=0+1=1
F3=1+1=2
F4=2+1=3
F5=3+2=5
....
Until F26=? (it's over 120000)
However, some smart mathematician found this following formula:
&phi=(1+sqrt(5))/2
Fn=(φ^n-(1-φ)^n)/sqrt(5)
Try both!
To find the number of ways 7 people can line up for plane tickets, we can use the concept of permutations. Permutations calculate the number of ways to arrange objects in a specific order.
In this case, we have 7 people who need to line up, and each person can take only one position in the line. Therefore, we need to find the number of arrangements for those 7 people.
To calculate the number of permutations, we multiply the number of choices at each position. Since each person in the line is unique, we have 7 choices for the first position, 6 choices for the second position (as one person has already taken the first position), 5 choices for the third position (as two people have already taken the first two positions), and so on.
Using the formula for permutations, we can calculate the total number of ways:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
Therefore, there are 5040 ways for 7 people to line up for plane tickets.