Prove that
` P(10,3)=P( 9,3) +3P ( 9,2)`

Prove that: P(1,1)+2. P(2,2)+3. P(3,3)++ndotP(n , n)=P(n+1,\ n+1)-1.

P(9,2) = P(x,2).Find x.

Prove that ^10P_3=^9P_3+3.^9P_2

Prove that 1+1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1).

If P(n) be the statement " 10n+3 is a prime number", then prove that P(1) and P(2) are true but P(3) is false.

P and Q are two element that form P_(2) Q_(3) and PQ_(2) . If 0.15 mole of P_(2) Q_(3) weighs 15.9 g and 0.15 mole of PQ_(2) weighs 9.3 g , what are the atomic weights of P and Q ?

If A and B are two events such that P(A//B)=p , P(A)=p , P(B)=1/3a n d\ P(AuuB)=5/9 then p= 2/3 b. 3/5 c. 1/3 d. 3/4

If (1-x+x^(2))^(4)=1+P_(1)x+P_(2)x^(2)+P_(3)x^(3)+...+P_(8)x^(8) , then prove that : P_(2)+P_(4)+P_(6)+P_(8)=40 and P_(1)+P_(3)+P_(5)+P_(7)=-40 .

If P(n) is the statement n^3+n is divisible by 3, prove that P(3) is true but P(4) is not true.

If A and B are two events such that P(A/B)=p,P(A)=p,P(B)= 1/3 and P(AcupB)=5/9 , then p is equal to ……. .