# Combination problems

#### David99

##### New member
1. In how many ways can 4 red balls, 3 white balls and 1 black ball be arranged in a line so that the black ball is always surrounded by a red and a white ball?
2. In how many ways can the balls be arranged if no red ball is next to a white?

#### Dr.Peterson

##### Elite Member
Please give it a try and show what you have done. That will give us a place to start from in helping you. Keep in mind that our purpose is to help you learn to solve the problem, not just to do it ourselves and show off our skill.

My first thought for (1) is to first choose a place for the black, then choose the order of the two balls around it, and then place the rest of the balls.

#### pka

##### Elite Member
1. In how many ways can 4 red balls, 3 white balls and 1 black ball be arranged in a line so that the black ball is always surrounded by a red and a white ball?
2. In how many ways can the balls be arranged if no red ball is next to a white?
$$\displaystyle r\,r\,r\,r\,b\,w\,w\,w\text{ Or }w\,w\,w\,b\,r\,r\,r\,r$$