# combinatorics question

Hi,
Need help with combinatorics question I stuck with.

In a group of 5 kids at school.
Every morning a kid choose in random a sandwich for that day.
The sandwiches options are: Chicken breast, Cheese, Egg, Jam

What is the probability that from any type of sandwich at least one a kid choose?
Original post by bracing-leash
Hi,
Need help with combinatorics question I stuck with.
In a group of 5 kids at school.
Every morning a kid choose in random a sandwich for that day.
The sandwiches options are: Chicken breast, Cheese, Egg, Jam
What is the probability that from any type of sandwich at least one a kid choose?

Just think abou the total number of possible kid-sandwich arrangements, then if all sandwich types are chosen so two kids must choose one type.

If youre having trouble getting started, maybe work it through for 3 kids, 2 sandwiches.
Hi,
Thanks.
Total is easy 4^5 = 1024

If all sandwich types are chosen so two kids must choose one type, so it is 5 on 2 = 10 possible combinations
than we have 4 sandwiches to choose from, so it is 10 * 4 = 40 possible combinations
than we are adding the order of the rest which is 3!, so 40 * 6 = 240 possible combinations
P = 240 / 1024

What do you think?
Original post by bracing-leash
Hi,
Thanks.
Total is easy 4^5 = 1024
If all sandwich types are chosen so two kids must choose one type, so it is 5 on 2 = 10 possible combinations
than we have 4 sandwiches to choose from, so it is 10 * 4 = 40 possible combinations
than we are adding the order of the rest which is 3!, so 40 * 6 = 240 possible combinations
P = 240 / 1024
What do you think?

Souds good.