Maharashtra Board Solutions for Chapter: Permutations and Combinations, Exercise 6: EXERCISE

Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear.

Find the number of triangles formed by joining $12$ points if no three points are collinear

Find the difference between the greatest values in the following:

${}^{15}C_{\mathit{r}}$ and ${}^{11}C_r$

A group consists of $9$ men and $6$ women. A team of $6$ is to be selected. How many of possible selections will have at least $3$ women?

A question paper has two sections. Section $\mathrm{I}$ has $5$ questions and section $\mathrm{II}$ has $6$ questions. A student must answer at least two question from each section among $6$ questions he answers. How many different choices does the student have in choosing questions?

There are $3$ wicket keepers and $5$ bowlers among $22$ cricket players. A team of $11$ players is to be selected so that there is exactly one wicketkeeper and at least $4$ bowlers in the team. How many different teams can be formed?

Five students are selected from $11$. How many ways can these students be selected if two specified students are selected?

Five students are selected from $11$. How many ways can these students be selected if two specified students are not selected?