Little Elephant and T-Shirts

Little Elephant and his friends are going to a party. Each person has his own collection of T-Shirts. There are 100 different kind of T-Shirts. Each T-Shirt has a unique id between 1 and 100. No person has two T-Shirts of the same ID. They want to know how many arrangements are there in which no two persons wear same T-Shirt. One arrangement is considered different from another arrangement if the