M L Aggarwal Solutions for Chapter: Permutations and Combinations, Exercise 8: EXERCISE 8.8

Find the number of combinations of four letters each that can be made from the letters of the word $\mathrm{TENNESSEE}$.

Find the number of permutations of four letters each that can be made from the letters of the word $\mathrm{TENNESSEE}$.

The crew of an eight-oar boat is to be chosen from $12$ men of whom three can row on the stroke side only. Find the number of ways in which crew can be arranged.

There are $n$ points in a plane, no three of which are collinear except $p$ points all of which are on a straight line. How many straight lines can be formed?

There are $n$ points in a plane, no three of which are collinear except $p$ points all of which are on a straight line. How many triangles can be formed out of these $n$ points?

A table has $7$ seats, $4$ being on one side facing the window and $3$ being on the opposite side. In how many ways can $7$ people be seated at the table if two people, $X$ and $Y$ must sit on the same side?

A table has $7$ seats, $4$ being on one side facing the window and $3$ being on the opposite side. In how many ways can $7$ people be seated at the table if $X$ and $Y$ must sit on opposite sides?

A table has $7$ seats, $4$ being on one side facing the window and $3$ being on the opposite side. In how many ways can $7$ people be seated at the table if $3$ people, $X,Y$ and $Z$ must sit on the side facing the window?