There are 4 parcels and 5 post offices. In how many ways can 4 parcels be got registered?

In how many ways can 5 keys be put in a ring?

Four books, one each in Accounting, Audit, Economics and Mathematics are to be arranged on shelf. In how many ways can this be done?

There are 12 seats in a mini bus and 8 persons are to be seated in it. In how many ways can they be seated?

A man has 7 friends. In how many ways he can invite one or more of them for a tea party

A family of 4 brothers and 3 sisters is to be arranged for a photograph in one row. In how many ways can they be seated if (i) all the sisters sit together, (ii) no two sisters sit together

There are 10 professors and 20 lecturers, out of whom a committee of 2 professors and 3 lecturers is to be formed. Find (i) In how many ways committee can be forms (ii) In how many ways a particular professsor is included (iii) In how many ways a particular lecturer is included (iv) In how many ways a particular lecturer is excluded