I have n values which are needed to categorize into m categories preserving a particular order.
Example
Monday- 13
Tuesday- 5
Wednesday- 4
Thursday- 4
Friday- 2
Saturday- 11
Sunday- 1
How can I categorize these 7 values to 5 groups preserving the order Mon, Tue, Wed, Thu, Fri, Sat, Sun
Best Answer
"How many ways can I put 4 barriers between 7 days (where no two barriers can be in the same place)?"
There are six positions... you want to choose 4 of them.
This can be done in "$6$ choose $4$" ways $\binom{6}{4}=15$ ways where $\binom{n}{k}$ denotes the binomial coefficient.