Question

how many different ways can 2 tickets be selected from 20 tickets if each ticket wins a different prize? each ticket wins the same prize ?

Answer 1

Solution:

Number of ways of selecting k objects from n distinct objects is given by,

We have 20 tickets and each tickets wins a different prize. It means we have 20 different tickets and we have to select 2 tickets.

Hence, number of ways of selecting 2 tickets from 20 tickets if each ticket wins a different prize is,

(Since, 20! = 20×19×18! and 2! = 2×1 = 2)

Hence, there are total 190 different ways by which 2 tickets can be selected from 20 tickets if each ticket wins a different prize.

Now if we have 20 tickets but each tickets wins the same prize, then it means that we have 20 tickets which are same. No matter which 2 tickets are selected, they wins the same prize.

Hence, if we concerned about the prize then number of ways of selecting 2 tickets from 20 tickets if each tickets wins the same prize is 1.