For the inter-hostel six-a-side football tournament, a team of 6 players is to be chosen from 11 players consisting of 5 forwards, 4 defenders and 2 goalkeepers. The team must include at least 2 forwards, at least 2 defenders and at least 1 goalkeeper. Find the number of different ways in which the team can be chosen.

The 12 houses on one side of a street are numbered with even numbers starting at 2 and going up to 24. A free newspaper is delivered on Monday to 3 different houses chosen at random from these 12. Find the probability that at least 2 of these newspapers are delivered to houses with numbers strictly greater than 14.

In the code fragment on the right, start and end are integer values and prime(x) is a function that returns true if x is a prime number and false otherwise. i := 0; j := 0; k := 0; for (m := start; m <= end; m := m+1){ k := k + m; if (prime(m)){ i := i + m; }else{ j := j + m; } } At the end of the loop:

Alan’s task is to design an algorithm for a decision problem P . He knows that there is an algorithm A that transforms instances of P to instances of the Halting Problem such that yes instances of P map to yes instances of the Halting Problem, and no instances of P map to no instances of the Halting problem. Which of the following is true.