Ben, Nhlanhla, Owen, Derick en 6 ander atlete neem aan 'n 100 m-resies deel - NSC Mathematics - Question 10 - 2018 - Paper 1

If 4 athletes need to be placed in adjacent lanes, we can treat them as a single block.

This gives us 7 blocks (the block of 4 athletes + the 6 remaining athletes).

Therefore, the number of ways to arrange these blocks is:

$7! = 5,040$

The number of ways to arrange the 4 athletes within the block is:

$4! = 24$

Thus, the total number of arrangements is:

$4! \times 7! = 120,960$

To find the probability that specific athletes are assigned to specific lanes:

The total number of ways to assign 10 athletes to 10 lanes is:

$10! = 3,628,800$

There is only 1 way to assign Ben to lane 1, Nhlanhla to lane 3, Owen to lane 5, and Derick to lane 7.

So, the probability is:

$P = \frac{1}{10!} = \frac{1}{3,628,800} = 0.0000002756$