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Odd and Even Numbers

Consider the ...

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Consider the set A= {345} and the number of null relations, identity relations, universal relations, reflexive relations on A are respectively n1, n2,n3, n4 then the value of n1+n2+n3+n4 is equal to 1) 8 2) 7 3) 73 4) 67

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Q. Consider the set

A = 3, 4, 5

and the numbers of null relations, identity relation, universal relations, reflexive relations on

A

are respectively

n_{1}, n_{2}, n_{3}

n_{4}

then the value of

n_{1} + n_{2} + n_{3} + n_{4}

5 < n_{1} < n_{2} < n_{3} < n_{4}

be integers such that

n_{1} + n_{2} + n_{3} + n_{4} = 35

. The number of such distinct arrangements

(n_{1}, n_{2}, n_{3}, n_{4})

.

n_{1} < n_{2} < n_{3} < n_{4} < n_{5}

be positive integers such that

n_{1} + n_{2} + n_{3} + n_{4} + n_{5} = 20

. Then the number of such distinct arrangements

(n_{1}, n_{2}, n_{3}, n_{4}, n_{5})

is .....................

n_{1} < n_{2} < n_{3} < n_{4} < n_{5}

be positive integers such that

n_{1} + n_{2} + n_{3} + n_{4} + n_{5} = 20

. Then the number of such distinct arrangements

(n_{1}, n_{2}, n_{3}, n_{4}, n_{5})

n_{1}

n_{2}

be the number of red and black balls, respectively in box I. Let

n_{3}

n_{4}

be the number of red and black balls, respectively in box II.
One of the two boxes, box I and box II was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II, is

\frac{1}{3},

then the correct option(s) with the possible values of

n_{1}, n_{2}, n_{3}

n_{4}

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