Date | May 2017 | Marks available | 5 | Reference code | 17M.1.hl.TZ1.4 |
Level | HL only | Paper | 1 | Time zone | TZ1 |
Command term | Find | Question number | 4 | Adapted from | N/A |
Question
Three girls and four boys are seated randomly on a straight bench. Find the probability that the girls sit together and the boys sit together.
Markscheme
METHOD 1
total number of arrangements 7! (A1)
number of ways for girls and boys to sit together =3!×4!×2 (M1)(A1)
Note: Award M1A0 if the 2 is missing.
probability 3!×4!×27! M1
Note: Award M1 for attempting to write as a probability.
2×3×4!×27×6×5×4!
=235 A1
Note: Award A0 if not fully simplified.
METHOD 2
37×26×15+47×36×25×14 (M1)A1A1
Note: Accept 37×26×15×2 or 47×36×25×14×2.
=235 (M1)A1
Note: Award A0 if not fully simplified.
[5 marks]