number puzzle

[bobobalde111]

john has started walking to work each day . the journey involves waling five streets south and three west but he likes to vary his route

how many different routes could he take without going out of his way

[crofter]

bob There are 56 different routes he could take!

The solution comes as the number of distinguishable arrangements there are of the sequence of eight symbols SSSSSWWW. This is given by 8! / 5! 3!, where 8! = 8 factorial = 8x7x6x ...2x1.

This count will cancel down to 8x7 = 56

[bobobalde111]

many thanks

where is julie fer this week

[juliefer]

I'm tempted to say that I thought I'd make crofter happy by letting him answer this one but actually I was too busy working to look at this site until well after crofter had answered. I wouldn't have been able to get the answer the 'proper' way in any case (I can do sums but not maths) or get it anything like as quickly as crofter must have done. Well done crofter and thank you from me too for the lucid explanation. Now you know you've got at least two fans on this site.