Embibe Experts Solutions for Exercise 8: Assignment

If $\sum _{k=0}^n\left(k^2+k+1\right)k!=\left(2007\right)·2007!$, then value of $n$ is

The number of six digit numbers that can be form from the digits $1,2,3,4,5,6$ and $7$. So that the digits do not repeat and the terminal digits are even is

The number of integers which lie between $1$ and ${10}^6$ and which have sum of the digits equal to $12$ is

$\sum _{r=0}^m{}^{n+r}C_n$ is equal to

Between two junction stations $A$ and $B$ there are $12$ intermediate stations. The number of ways in which a train can be made to stop at $4$ of these stations so that no two of these halting station are consecutive is

$m$ parallel lines in a plane are intersected by family of $n$ parallel lines. The total number of parallelogram so formed is

There are $n$ straight lines in a plane, no two of which are parallel and no three pass through the same point. Their point of intersection are joined. Then the number of fresh lines thus obtained is

On the modified chess board $10\times 10$, Amit and Suresh two persons which start moving towards each other. Each person moving with same constant speed. Amit can move only to the right and upwards along the lines while Suresh can move only to the left or downwards along the lines of the chess board. The total number of ways in which Amit and Suresh can meet at same point during their trip is