Answer:
The number of ways the bus can be filled is 28 ways
Step-by-step explanation:
The given parameters are;
The number of seats in the bus = 6
The number of passengers available = 8
The number of ways the bus can be filled involve the number of ways of selecting from the 8 passengers taking 6 at a time given as follows;
The combination of n items, taking n items, taking r at a time is [tex]_nC_r[/tex] which can be given as follows;
[tex]_nC_r = \dfrac{n!}{r! \cdot (n - 1)}[/tex]
Therefore;
The number of ways the bus can be filled is therefore;
[tex]_8C_6 = \dfrac{8!}{6! \times (8 - 6)!}= \dfrac{8!}{6! \times 2!} = \dfrac{8 \times 7}{2 \times1} = 28 \ ways[/tex].
