Permutations and Combinations
The number of different words that can be formed using all the letters of the letters of the word COCACOLA with start and ends with O is
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denote the number of ways in which k
identical balls can be colored with n
colors so that there is at least one ball of each color. Then f(2n,n)
must be equal to
a. 2nCn b. 2n−1Cn+1
c. 2n−1Cn d. none of these
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
Number of ways in which 200 people can be divided in 100 couples is a. 2100(100!)(200)! b. 1×3×5××199 c. (2101)(2102)………….(2200)
There are always 4 letters between P and S?
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
There are 10 points in a plane of which no three points are collinear and four points are concyclic. The number of different circles that can be drawn through at least three points of these points is (A) 116 (B) 120 (C) 117 (D) none of these
Kanchan has 10 friends among whom two are married to each other. She wishes to invite five of them for a party. If the married couples refuse to attend separately, then the number of different ways in she can invite five friends is
c. 10C5−2×8C4 d. none of these
Evaluate (n−r)!n!, when(i) n=6,r=2.