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Permutation and Combination
31.The number of positive integer solutions for the equation x + y + z = 20 where x ≥ 2, y ≥ 3, z ≥ 4 is _______.
32. There are 3 groups A, B and C –with 8, 6 and n persons respectively. Each person in a group shakes hands with every person in the other groups exactly once and no two persons within a group shake hands. The total number of handshakes among them is 104. Find the value of n.
33. Fifteen lines are drawn in a plane such that four of them are parallel. What is the maximum number of regions into which the plane is divided?
34. Four athletes Pravin, Visharath, Bhushan and Durandhar participate in 6 athletic events. There is only one prize for winning in each event and each of them won in at least one event. In how many ways could they have won the six prizes?
35. There are 6 letters and corresponding 6 addressed envelopes. If the letters are placed into the envelopes randomly (each letter is placed only in one envelope), in how many ways can exactly two letters be placed into their corresponding envelopes?
