Popular Combinatorics Questions

Q.1 In how many ways can clean & clouded (overcast) days occur in a week assuming that an entire day is either clean or clouded. Q.2 Four visitors A , B , C & D arrive at a town which has 5 hotels . In how many ways can they ...

A flight of stairs has 10 steps. A person can go up the steps one at a time, two at a time, or any combination of 1's and 2's. Find the total number of ways in which the person can go up the stairs. ...

If A = {1,2,3,4....18,19} then the number of functions f : A→A such that f(x)=y and sum of digits of x is equal to the sum of digits of y is (a) 540 (b) 219 (c) 218 (d) 720 ...

There are three coplanar parallel lines.If any p points are taken on each of the line,the maximum number of triangles with vertices at these points is a.3p2(p-1) b.3p2(p-1)+1 c.p2(4p-3) d.None of these ...

in how many ways we can make a 4 digit no. using 1,2,3,4 and what's the sum of all the numbers obtained?(repeatations not allowed) ...

Three distinct numbers are selected uniformly at random from the ten-term geometric sequence with first term 10/9 and common ratio 2 . What is the expected value of their sum? ...

\hspace{-16}$In how many ways can the selection of $\bf{8}$ letters be done frm $\bf{24}$ letters\\\\ of which $\bf{8}$ are $\bf{'a'}$ and $\bf{8}$ are $\bf{'b'}$ and rest are unlike. ...

What would be the sum of nck + nc2k + nc3k + nc4k ...

Number of zeroes at the end of the number Î rr where r varies from 1 to 25, is (a) 50 (b) 49 (c) 49 (d) 100 ...

Three children,each accompanied by a guardian,seek admission in a school.The principal wants to interview all the 6 persons one after the other,subject to the condition that no child is interviewed before its guardian.In how ...

number of permutations of taken all at a time such that the digit 1,2,3,4,5,6,7,8,9 appearing somewhere to the left of 2. 3 appearing to the left of 4. 5 appearing to the left of 6. eg 815723946 ...

If m men and n women are to be seated in a row such that no two women seat together,then find the ways in this can be done. ...

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There are 5 different red balls,5 different green balls,5 different blue balls and 5 different black balls.In how many ways can they be arranged so that no two balls of same color are adjacent ? ...

\hspace{-16}\bf{(1)\;\;}$ Total Integer ordered pair,s of $\bf{(x,y)}$ in $\bf{x^2-y! = 2001}$\\\\\\ $\bf{(2)\;\;}$ Total Integer ordered pair,s of $\bf{(x,y)}$ in $\bf{x^2-7y! = 2011}$\\\\\\ $\bf{(3)\;\;}$ Total Integer orde ...