Theory question 106
Permutations and Combinations(a) Evaluate 9P3/15C3 + 5C3/3P2 correct to two decimal places.
(b) A committee of 2 tutors and 5 pupils is to be formed among 6 tutors and 10 pupils. In how many ways can this be done, if one particular tutor must be on the committee and two particular pupils must not be on the committee?
Show the model answer
Model answer
(a) 9P3 = 504, 15C3 = 455, 5C3 = 10, 3P2 = 6
504/455 + 10/6 = 1.1077 + 1.6667 = 2.77 (2 d.p.)
(b) The particular tutor is in; choose 1 more tutor from the other 5: 5 ways
Leave out the 2 particular pupils; choose 5 pupils from 8: 8C5 = 56 ways
Number of committees = 5 × 56 = 280
Explanation
Remove the people whose places are already decided, then choose from those left.