O-LevelAdditional MathematicsPermutations and combinations4037/22 · Oct/Nov 2011 · Q56 Marks
Four boys and three girls are to be seated in a row. Calculate the number of different ways that this can be done if
- (i)the boys and girls sit alternately,[2]
- (ii)the boys sit together and the girls sit together,[2]
- (iii)a boy sits at each end of the row.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [M1] (i) Evidence of 4 × 3 × 3 × 2 × 2(× 1 × 1) or 4! × 3!
- [A1] (i) 144
- [M1] (ii) 4! (or 24) for boys and 3! (or 6) for girls
- [A1] (ii) 288
- [M1] (iii) Evidence of 4 × (120) × 3 or (4) × 5! × (3)
- [A1] (iii) 1440
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →