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 all of the boxes of each type of cereal are together?

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