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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

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Important Questions on Permutation and Combination

HARD
JEE Main/Advance
IMPORTANT
Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1-Tn=10, then the value of n is 
MEDIUM
JEE Main/Advance
IMPORTANT
The number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition is
HARD
JEE Main/Advance
IMPORTANT
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is
HARD
JEE Main/Advance
IMPORTANT
A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then, the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is 
MEDIUM
JEE Main/Advance
IMPORTANT
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a  shelf so that the dictionary is always in the middle. The number of such arrangements is
HARD
JEE Main/Advance
IMPORTANT
Let S be the set of all triangles in the x y- plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is 
MEDIUM
JEE Main/Advance
IMPORTANT
Consider three boxes, each containing 10 balls labelled 1,2,,10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the i th box, (i=1,2,3) . Then, the number of ways in which the balls can be chosen such that n1<n2<n3 is 
HARD
JEE Main/Advance
IMPORTANT
How many positive integers are there such that n is a divisor of one of the numbers 1040, 2030 ?