Theory question 105
Permutations and Combinations(a) There are six points in a plane. How many triangles can be formed with the points?
(b) A family of six is to be seated in a row. In how many ways can this be done, if the father and mother are not to sit together?
Show the model answer
Model answer
(a) Any 3 of the 6 points (no three in a line) make a triangle: ⁶C₃ = 20 triangles
(b) All arrangements: 6! = 720
Father and mother together (treat as one unit, 2 orders): 2 × 5! = 240
Not together: 720 − 240 = 480 ways
Explanation
For 'not together', subtract the 'together' arrangements from the total.