Let Xn - 1-2-3-n and let a subset A of Xn be chosen so that every pair of elements of A differ by at least 3- For example- if n - 5- A can be - 2 or 1-5 among others- When n - 10- let the probability that 1 - A be p and let the probability that 2 - A be q- Then

Let $p, q$ be integers and let $α, β$ be the roots of the equation $x^{2} - 2 x + 3 = 0$ where $α \neq β .$ For $n = 0, 1, 2, . . .,$ let $a_{n} = p α^{n} + q β^{n}$ and $a_{3} = - 10,$ then $p^{q} + q^{p} =$ ___

Q. Let A be a set containing n elements. A subset P of the set A is chosen at random.The set A is reconstructed by replacing the elements of

P

and another subset

Q

of A is chosen at random. The probability that

P \cap Q

contains exactly

m (m < n)

elements is

Q. Let

A

be a set containing

n

elements. A subset

P

of the set

A

is chosen at random.
The set

A

is reconstructed by replacing the element of

P

, and another subsets

Q

A

is chosen at random. The probability that

(P \cap Q)

contains exactly

m (m < n)

elements is

Q. A is a set containing n elements. Two subsets P and Q of A are chosen at random. (P and Q may have elements in common). The probability that

P \cup Q \neq A

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Let Xn = {1,2,3,.n) and let a subset A of Xn be chosen so that every pair of elements of A differ by at least 3. (For example, if n = 5, A can be ϕ, {2} or {1,5} among others). When n = 10, let the probability that 1∈A be p and let the probability that 2∈A be q. Then

Let $X_{n}$ = {1,2,3,.n) and let a subset A of $X_{n}$ be chosen so that every pair of elements of A differ by at least 3. (For example, if n = 5, A can be $ϕ$ , {2} or {1,5} among others). When n = 10, let the probability that $1 \in A$ be p and let the probability that $2 \in A$ be q. Then