Permutations
Permutations - The different arrangements that can be made with a given number of things taking some or all of them at a time are called permutations. The symbol n P r or P(n,r) is used to denote the number of permutations of n things taken r at a time..
Example 2:
In how many different arrangements can 6 gentlemen and 6 ladies sit around a table if i) there is no restriction and ii) no two ladies sit side by sid..
Theorem:
The number of combinations of n dissimilar things, taken r at a time is..
The number of combinations of n dissimilar things, taken r at a time is..Combinations
Combinations - The selection of a number of things taking some or all of them at a time are called combinations. The number of ways of selecting r things out of n dissimilar things is denoted by C(n, r) or n C ..
Question 7
Question: Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Find the number of words which have atleast one letter repeated. Answer: Total number of 5 letter words from given 10 letters = 10 5 (if every letter may be repeated a..
Combinations
The selection of a number of things taking some or all of them at a time are called combinations. The number of ways of selecting r things out of n dissimilar things is denoted by C(n, r) or n C r..
Properties of Determinants
If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) tim..
If the rows and columns of a determinant are inter-changed, the value remains unaltered. If any two rows (columns) of a determinant are identical, its value of the determinant is zero. If any two rows (columns) of a determinant are interchanged, the value of the determinant is (-1) tim..Permutations and Combinations Introduction
Summary - The fundamental principle of counting (F.P.C) states that if an operation can be performed in m different ways and if for each such choice, another operation can be performed in n different ways, then both operations, in succession can be performed in exactly mn different ways. The princi..
Proof:
The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any one..
The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any one..Co-factors
The co-factor of the element a ij is (-1) i+j times its minor a ij . We shall denote the cofactor of an element by the corresponding capital letter. Cofactor of a i j = A i j = (-1) i + j M i j Consider the determinant The minor of a 1 1 can be obtained by deleting the fir..
The co-factor of the element a ij is (-1) i+j times its minor a ij . We shall denote the cofactor of an element by the corresponding capital letter. Cofactor of a i j = A i j = (-1) i + j M i j Consider the determinant The minor of a 1 1 can be obtained by deleting the fir..See what our Users say :
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