Permutations and Combinations
The number of permutation of letters a,b,c,d such that b does not follow a and c does not follow b andd does not follow c is
The total number of positive integral solution of 15<x1+x2+x3≤20 is equal to a. 685 b. 785 c. 1125 d. none of these
The number of different ways in which five "alike dashes" and "eight alike" dots can be arranged using only seven of these "dashes" and "dots" is a. 350 b. 120 c. 1287 d. none of these
m men and n women are to be seated in a row so that no two women sit together. If (m>n) then show that the number of ways in which they can be seated as (m−n+1)!m!(m+1)! .
Let f(n) be the number of regions in which n coplanar circles can divide the plane. If it is known that each pair of circles intersect in two different points and no three of them have common points of intersection, then (i) f(20)=382 (ii) f(n) is always an even number (iii) f−1(92)=10 (iv) f(n) can be odd
Find the number of three-digit numbers from 100 to 999 including all numbers which have any one digit that is the average of the other two.
If the number of selections of 6 different letters that can be made from the words SUMAN and DIVYA so that each selection contains 3 letters from each word is N2, then the value of N is________.