Permutations and Combinations
If 6!1+7!1=8!x, find x.
Let n be a four-digit integer in which all the digits are different. If x is number of odd integers and y is number of even integers, then a. x<y b. x>y c. x+y=4500 d. ∣x−y∣=54
A variable name in certain computer language must be either an alphabet or an alphabet followed by a decimal digit. The total number of different variable names that can exist in that language is equal to a. 280 b. 390 c. 286 d. 296
Number of points of intersection of n straight lines if n satisfies n+5Pn+1=211(n−1)×n+3Pn is a. 15 b. 28 c. 21 d. 10
The streets of a city are arranged like the like the lines of a chess board. There are m streets running from north to south and n streets from east to west. Find the number of ways in which a man can travel from north-west to south-east corner, covering shortest possible distance.
There are 20 books on Algebra and Calculus in one library. For the greatest number of selections each of which consists of 5 books on each topic. If the possible number of Algebra books are N, then the value N/2 is __________.
Statement 1: number of ways in which 10 identical toys can be distributed among three students if each receives at least two toys is 6C2˙ Statement 2: Number of positive integral solutions of x+y+z+w=7is6C3˙