Photo AI
5 Lev (L), Maria (M) and Nicholas (N) sit in a row of three seats - OCR - GCSE Maths - Question 5 - 2019 - Paper 1
Question 5
5 Lev (L), Maria (M) and Nicholas (N) sit in a row of three seats. (a) Use the table to list all the different orders in which they could sit. One possible order is... show full transcript
Worked Solution & Example Answer:5 Lev (L), Maria (M) and Nicholas (N) sit in a row of three seats - OCR - GCSE Maths - Question 5 - 2019 - Paper 1
Step 1
Use the table to list all the different orders in which they could sit.
Answer
To determine the different orders, we can permute the seating arrangements of Lev (L), Maria (M), and Nicholas (N). The total possible arrangements (permutations) of 3 people are calculated as follows:
The seating arrangements are:
- L, M, N
- L, N, M
- M, L, N
- M, N, L
- N, L, M
- N, M, L
These will be filled in the table as:
| Seat 1 | Seat 2 | Seat 3 |
|---|---|---|
| L | M | N |
| L | N | M |
| M | L | N |
| M | N | L |
| N | L | M |
| N | M | L |
Step 2
What is the probability that Lev (L) sits next to Maria (M)?
Answer
To find the probability that Lev (L) is next to Maria (M), we first list the arrangements where they sit together:
- L, M, N
- M, L, N
- N, L, M
- L, N, M (not counted)
- N, M, L (not counted)
- M, N, L (not counted)
The acceptable arrangements are those where L and M are adjacent:
- L, M, N
- M, L, N
- N, L, M
Thus there are 3 favorable outcomes. Since there are 6 total possible arrangements, the probability is given by:
Therefore, the probability that Lev (L) sits next to Maria (M) is (\frac{1}{2}).