Combinatorics

Question

Sanjay have 9 distinct paths (1,2,3.....,9) from his home to his work place. He works from Monday to Friday every week, he does not go to work on Saturdays and Sundays. Every Sunday he schedules that which path he will take for each day for the coming week. The only restriction is that he cannot select even number paths on 2 consecutive days. How many possible combinations he have to make his schedule?

Comments

29225??

---

@  Mk Utkarsh ..is the answer 62520? please tell :)

Answer 1

is answer 29225?

since it asks only for 5 working days ( monday , tuesday , wednesday , thursday, friday)

so lets start with monday = 2 choices ( start with odd no. or with even no.) so "4" choices for even( days numbered 2,4,6,8) and "5" choices for odd(1,3,5,7,9) .

now you can draw a tree like structure

now the only restriction here is that after every 4(means you have selected a even numbered day) put 5 , but after every 5(means you have selected a odd numbered day)you have all (1 to 9 possiblities).

At the end i have added all possiblities.

Answer 2

......

Comments

 ankitgupta.1729 how you are calculating values?

---

@once_2019 ,here Days represent levels of the tree..So , for each level either we have 5 choices or 4 choices..So, go from monday to friday by each path of the tree and multiply all the choices...In the end , sum all the values which we get from each path of the tree..