In how many ways can 6 people be lined up to get on a bus?

Question

Avery Alexander · Accepted Answer

#6! = 720# #6# choices for the first person; #color(white)("XX")#for each of these, #5# choices for the next; #color(white)("XXXX")#for each of these, #4# choices for the next; #color(white)("XXXXXX")#for each of these, #3# choices for the next; #color(white)("XXXXXXXX")#for each of these, #2# choices for the next; #color(white)("XXXXXXXXXX")#for each of these, #1# choice for the last person. #6xx5xx4xx3xx2xx1 = 6! = 720#

Eli Assouline · Answer

undefined The number of ways 6 people can be lined up to get on a bus is calculated using the concept of permutations.

In permutations, the number of ways to arrange $n$ distinct objects is given by $n!$, where $n$ factorial is the product of all positive integers up to $n$.

So, for 6 people to line up to get on a bus, the number of ways is:
$$6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$$

Therefore, there are 720 ways for 6 people to line up to get on a bus.

Eva Adamson · Answer

undefined The number of ways 6 people can be lined up to get on a bus is calculated using the permutation formula, which is n! (n factorial), where n represents the number of people.

Therefore, for 6 people:

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

So, there are 720 ways in which 6 people can be lined up to get on a bus.