Maharashtra Board Solutions for Chapter: Permutations and Combinations, Exercise 7: MISCELLANEOUS EXERCISE

A question paper has $6$ questions. How many ways does a student have to answer if he wants to solve at least one question?

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

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.

Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed.

There are $12$ distinct points $A, B, C, ....., L$ in order, on a circle. Lines are drawn passing through each pair of points. How many lines are there in total.

There are $12$ distinct points $A, B, C, .....,L$ in order, on a circle. Lines are drawn passing through each pair of points. How many lines pass through $D$.

There are $12$ distinct points $A, B, C, ....., L$ in order, on a circle. Lines are drawn passing through each pair of points. How many triangles are determined by lines.

There are $12$ distinct points $A, B, C, ....., L$ in order, on a circle. Lines are drawn passing through each pair of points. How many triangles have on vertex $C$.