IISc (CDS-CS) Bangalore | CDS-CS Written | Sample Question: 4

Question

Anand is preparing a pizza with $8$ slices, and he has $10$ toppings to put on the pizza. He can put only one topping on each slice but can use the same topping on zero or more slices. In how many unique ways can he prepare the slices so that the same topping is not used in adjacent slices?

Answer 1

Let the slices of pizza be S1, S2 , S3 , ... S8

So for S1 we have 10 topping options

and for S2 we have 9 topping options , as can't use 10th topping . otherwise  two adjecent slice will have same topping .

 similarly S3 have 9 options ,

and S4 , S5 .. S7 have 9 options .

But S8 have only 8 options for topping as it is adjecnt to S1 and S7 .

So total unique ways can he prepare the slices = 10*(9^6)*8