# Bus Stops

• Jan 29th 2007, 12:16 PM
thefirsthokage
Bus Stops
A school bus starts with 6 kids at the academy and would stop at 5 places on its designated route. (Each of the 6 kids would get off at one of the 5 places)

a) In how many ways can all the kids get off the bus?

b) How many ways are there if no one leaves at the 2nd and 3rd stop?
• Jan 29th 2007, 12:35 PM
Plato
The answer to part (a) is the number of mappings from a set of six to a set of five.

The answer to part (b) is the number of mappings from a set of six to a set of three.
• Jan 29th 2007, 01:16 PM
Soroban
Hello, thefirsthokage!

You can baby-talk your way through these . . .

Quote:

A school bus starts with 6 kids and stops at 5 places on its route.
. . (Each of the 6 kids would get off at one of the 5 places.)

We'll assume that the six children are distinguishable,
. . that they have different names: $A,\,B,\,C,\,D,\,E,\,F$.

Quote:

a) In how many ways can all the kids get off the bus?

Consider:
. . $A$ can get off at any of the 5 places: $5\text{ choices.}$
. . $B$ can get off at any of the 5 places: $5\text{ choices.}$
. . $C$ can get off at any of the 5 places: $5\text{ choices.}$
. . . . . and so on.

Therefore, there are: . $5^6\:=\:15,625\text{ ways.}$

Quote:

b) How many ways are there if no one leaves at the 2nd and 3rd stops?

If no one leaves at the 2nd and 3rd stop, they each have three choices.

Therefore, there are: . $3^6 \:=\:720\text{ ways.}$