# Holi problem

**Discrete Mathematics**Level pending

It was holi.Five of my friends Harsh, Tavish , Vaibhav, Abhinav and Ambuj were walking through a lane. In the lane 10 of our friends were waiting for them with their watergun and water balloons.Harsh didn't want to get wet.

Let the number of ways in which Harsh didn't get wet be \(d^{e}\).[where d is a square of prime number ]

Let \(5^{a}\times c \) be the number of ways in which at least one of them didn't get wet.

Then find (a+c)-(d+e).

**DETAILS and ASSUMPTIONS**

Each of the friend can throw water on any of the five. The 10 friends will not prejudice on the basis that any of the five friends are wet or not.In other words probability of each of the 5 friends to get hit by any of the other 10 in the lane is same.Each of the 10 friends will throw water on only one boy.And yes each one will throw water.

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