Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5.

Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.

Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 8 green balls, and 7 blue balls so that 3 balls of every colour are drawn.

In a group of 20 adults, there are 8 males and 9 vegetarians. Find the number of female non vegetarians, if the group contains 5 male vegetarians ?

The total number of ways of answering 5 objective type questions, each question having 4 choices, is

There are 4 doctors and 8 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.