Answer the following questions : If m things are distributed among a men and women, show that the probability of receiving odd number of things by 'men is `1/2[((b+a)^m - (b-a)^m)/(b+a)^m]`.

If n things are arranged at random in a row then the probability that m particular things are never together is -

A coin is tossed (m + n) times (m gtn). Show that the probability of at least m consecutive heads is (n+2)//2^(m+2).

A committee of two persons is selected from two men and two women. What is the probability that the committee will have (a) no man? (b) one man? (c) two men?

Number of ways in which 30 identical things are distributed among six persons is a .^17C_5 if each gets odd number of things b .^16C_11 if each gets odd number of things c .^14C_5 if each gets even number of things (excluding 0) d .^15C_10 if each gets even number of things (excluding 0)

Find the number of ways in which n different prizes can be distributed among m(< n) persons if each is entitled to receive at most n-1 prizes.

Find the number of permutations of n different things taken r at time so that m(ltr) particular things will never occur.

Answer any Two questions : In triangle ABC angle C = 90^@ , If BC = m and AC = n then prove that m sin A+ n sin B = sqrt(m^2+ n^2)

In a game called odd man out m(m >2) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is (A) 1/(2m) (B) m/2^(m-1) (C) 2/m (D) none of these

If a body weighs m_1 gm-wt in air of density d and m_2 g-wt in a liquid of density D show that the density of the material of the body = ((m_1D)/(m_1-m_2)-(m_2d)/(m_1-m_2))gm//cm^2 .