There are 10 persons named `P_1,P_2,P_3,……….,P_10`. Out of 10 persons, 5 periods are to be arranged in a line such that in each arrangement `P_1` must occur whereas `P_4 and P_5` do not occur. Find the number of such positive arrangements.

Find the number of arrangements of the letters of the word ‘INDEPENDENCE’. In how many of these arrangements, do the words start with P ?

Perimeter of a triangle is 6p ^(2) - 5p + 10 and two and sides of the triangle are p ^(2) + p -2 and 2p ^(2) - 3p + 5. Find the third side of the triangle.

Given P(A)=3/5 and P(B)=1/5 . Find the P(AcupB) if A and B are mutually exclusive events.

Figure EP 10.5 shows a standard two slit arrangement with slits S_1 , S_2 , P_1 , P_2 are the two minima points on either side of P. At P_2 on the screen, there is a hole and behind P_2 is a second 2-slit arrangement with slits S_3 , S_4 and a second screen behind them.

Find the number of arrangements of the letters of the word ‘INDEPENDENCE’. In how many of these arrangements, do the words begin with I and end in P ?

If p = – 10, find the value of p^2 – 2p – 100

Given P(A) =3/5 and P(B) =1/5. Find P(A or B), if A and B are mutually exclusive events.

Given that the events A and B are such that P(A) = 1/2, P(AcupB)=3/5 and P(B) = p .Find p if they are independent.

Given that the events A and B are such that P(A)=1/2 , P(AcupB)=3/4 and P(B)=p. find p if they are independent.