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4866
narsingh deo
In a village there are equal no of boys and girls of marriageable age.Each boy dates a certain no. of girls and each girl dates a certain number of boys,under what condition is it possible that every girl and boy gets married to one of their dates?
In a village there are equal no of boys and girls of marriageable age.Each boy dates a certain no. of girls and each girl dates a certain number of boys,under what cond...
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2 answers
4867
Discrete math
The following is a sequence of formula, ... $10$. (a) Establish a formula in $\sum$ notation. (b) Generalize that formula in for any base $b$..
The following is a sequence of formula,$$\begin{align*} \begin{matrix} & 9*1+2 &= &11 \\ & 9*12+3 &= &111 \\ & 9*123+4 &= &1111 \\ & 9*1234+5 &= &11111 \\ \end{matrix} \\...
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3 votes
2 answers
4868
Manipulation of sum
Prove the identity: $\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\right ) \end{align*}$
Prove the identity:$$\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\...
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0 votes
2 answers
4869
Discrete Math
Prove or disprove: $\begin{align*} \log_8x = \frac{1}{2}.\log_{2}x \end{align*}$.
Prove or disprove: $\begin{align*} \log_8x = \frac{1}{2}.\log_{2}x \end{align*}$.
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1 votes
1 answer
4870
the number of ways in which 4 distinct balls
the number of ways in which 4 distinct balls can be put in 4 boxes labelled a,b,c,d such that b does not follow a, and c does not follow b, and d does not follow c,is
the number of ways in which 4 distinct balls can be put in 4 boxes labelled a,b,c,d such that b does not follow a, and c does not follow b, and d does not follow c,is
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0 votes
2 answers
4871
A closet has 5 pair of shoes.
A closet has 5 pair of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is
A closet has 5 pair of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair is
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4872
The number of ways of seating three gentlemen
The number of ways of seating three gentlemen and three ladies in a row, such that each gentlemen is adjacent to atleast one lady.
The number of ways of seating three gentlemen and three ladies in a row, such that each gentlemen is adjacent to atleast one lady.
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2 votes
1 answer
4873
C. L. Liu 3.38(b)
Among $3n + 1$ objects, $n$ of them are identical. Find the number of ways to select $n$ objects out of these $3n + 1$ objects.
Among $3n + 1$ objects, $n$ of them are identical. Find the number of ways to select $n$ objects out of these $3n + 1$ objects.
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4874
Let X={a1,a2,...,a7} be a set of seven elements and Y={b1,b2,b3} a set of three elements.
Let X={a1,a2,...,a7} be a set of seven elements and Y={b1,b2,b3} a set of three elements. The number of functions f from X to Y such that {i} f is onto and {ii}there are exactly three statements x in X such that f(x)=b1,is
Let X={a1,a2,...,a7} be a set of seven elements and Y={b1,b2,b3} a set of three elements. The number of functions f from X to Y such that {i} f is onto and {ii}there are ...
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2 votes
1 answer
4875
let S={1,2,...,100}.
let S={1,2,...,100}. The number of nonempty subsets A of S such that the product of elements in A is even is
let S={1,2,...,100}. The number of nonempty subsets A of S such that the product of elements in A is even is
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1 votes
1 answer
4876
The number of functions f from
The number of functions f from {1,2,...,20} into {1,2,....,20} such that f(k) is a multiple of 3 whenever k is a multiple of 4 is
The number of functions f from {1,2,...,20} into {1,2,....,20} such that f(k) is a multiple of 3 whenever k is a multiple of 4 is
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1 votes
1 answer
4877
consider the quadratic equation of the form x2+bx+c=0
consider the quadratic equation of the form x2+bx+c=0.The number of such equations that have real roots and coefficients b and c from the set{1,2,3,4,5} (b and c may be equal) is
consider the quadratic equation of the form x2+bx+c=0.The number of such equations that have real roots and coefficients b and c from the set{1,2,3,4,5} (b and c may be e...
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0 votes
1 answer
4879
Maths
There are 11 points on a plane with 5 lying on one straight line and another 5 lying on other straight line which is parallel to the first line. The remaining point is not collinear with any two of the previous points.The number of triangles that can be formed with vertices chosen from these 11 points is
There are 11 points on a plane with 5 lying on one straight line and another 5 lying on other straight line which is parallel to the first line. The remaining point is no...
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1 votes
1 answer
4880
In a multiple-choice test there are 6 questions.
In a multiple-choice test there are 6 questions. 4 alternatives answers are given for each question by choosing one answer for each question, then the number of ways to get exactly 4 correct answers is (A) ; (B) 135; (C) 9; (D) 120.
In a multiple-choice test there are 6 questions. 4 alternatives answers are given for each question by choosing one answer for each question, then the number of ways to g...
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