What day of the week is July 4th?
What day of the week is July 4th? => Monday or Friday or Sunday or Tuesday..
Discrete Mathematics - Test Questions I
Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..
Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..Verification by numerical problems
\ A + B = B + A \ A + B = B ..
\ A + B = B + A \ A + B = B ..To find the sum of a number of terms in Arithmetical Progression:
Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..
Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..To find the nth term of an H.P
To find the n t h term of an H.P, find the n t h term of the corresponding A.P. obtained by the reciprocals of the terms of the given H.P. Now the reciprocal of the n t h term of an A.P. will be the n t h term of the H...
To find the nth term of a GP, whose first term is a common ratio r and number of terms is n
We observe that the index of r on the right hand side is one less than the suffix of t on the left hand side in each of the equalities. Hence t n = ar n - 1 which is the general term of the given G..
We observe that the index of r on the right hand side is one less than the suffix of t on the left hand side in each of the equalities. Hence t n = ar n - 1 which is the general term of the given G..Introduction
Arrangement and selection of objects are the central ideas of this chapter on permutations and combinations. They are widely applied in solving problems of probability, genetic engineering and life scienc..
Introduction
Arrangement and selection of objects are the central ideas of this chapter on permutations and combinations. They are widely applied in solving problems of probability, genetic engineering and life science..
Matrices, Determinants Conclusion
Conclusion - We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan metho..
Proof:
Each circular permutation corresponds to n linear permutations depending on where we start. Since there are exactly n! linear permutations, there are exactly permutations. Hence, the number of circular permutations is the same as (n-1)..
Each circular permutation corresponds to n linear permutations depending on where we start. Since there are exactly n! linear permutations, there are exactly permutations. Hence, the number of circular permutations is the same as (n-1).. Result
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