Week 278 (16th December 2022)

Holly is really excited for Christmas and has been enjoying the count down to the big day by opening her advent calendar each morning.

It’s now the week before Christmas and the advent calendar has 4 milk chocolates, one plain chocolate and two white chocolates left in it. 

Holly has taken a sneaky look and knows there is a milk chocolate in the 18th December and a plain chocolate for the 24th December.  

How many ways can the seven chocolates be arranged? 


So with the plain chocolate being on 24th and one of the milk chocolates being on 18th, we have 5 chocolates to arrange over 5 days.  Assuming each type of chocolate is identical, then they can be arranged in the following ways: 

  1. MMMWW 
  2. MMWMW 
  3. MWMMW 
  4. WMMMW 
  5. WMMWM 
  6. WMWMM 
  7. WWMMM 
  8. MWWMM 
  9. MMWWM 
  10. MWMWM 

So there are 10 ways the seven chocolates can be arranged.