A store clerk is stocking a shelf with boxes of cereal Suppo

A store clerk is stocking a shelf with boxes of cereal. Suppose that the clerk has 3 boxes of Fruit Loops, 5 boxes of Trix, and 4 boxes of Fruity Pebbles. Boxes of the same brand of cereal look the same.

- What is the probability that no boxes of Fruit Loops are next to each other?

Solution

e) there are 3 types of cereals so 3!.

3 boxes of Fruit loops cna be arranged in 3! ways

5 boxes of trix can be arranged in 5! ways

4 boxes of fruity pebbles can be arranged in 4! ways

total 12 boxes can be arranged in 12! ways

Prob=3!*3!*5!*4!/12!=0.00021

f) first arrange fruits loops together. this cna be done in 3! ways. now consider this as one unit. then 5 boxes of trix and 4 boxes of fruity pebbles with this 1 unit can be arranged in 5+4+1=10 10! ways. so total number of outcomes=4!*10!

Prob(fruity loops are together)=4!*10!/12!=0.1818

P(fruity are not togheter)=1-0.1818=0.8181