Permutations and Combinations
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word'EXAMINATION' is _______
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Prove by combinatorial argument that .n+1Cr=nCr+nCr−1˙
How many chords can be drawn through 21 points on a circle?
ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked on the sides AB, BC, CD, and DA, respectively. The number of triangles with vertices on different sides is (A) 270
(B) 220 (C) 282 (D) 342
How many five-digit numbers can be made having exactly two identical digits?
Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that(i) all vowels occur together (ii) all vowels do not occur together.
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
A batsman scores exactly a century by hitting fours and sixes in 20 consecutive balls. In how many different ways can he do it if some balls may not yield runs and the order of boundaries and over boundaries are taken into account?
A number of 18 guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.