Suppose you ask five random people to each pick a number between 1 and 10, and they don't get to hear what the other people are saying.

What are the chances that 4 even numbers are picked, followed by 1 odd number, and that none of them chose the same number.

For the first number picked there is a 5/10 chance that it will be even.

For the second number picked there is a 4/10 chance that it will be even AND different to the previous numbers.

For the third number there is a 3/10 chance that it will be even and different.

For the fourth number there is a 2/10 chance that the number will be even and different, and finally

for the fifth number there is a 5/10 chance that it will be odd (and if so is clearly different to the previous numbers).

The chance of all these being true is:

5/10 * 4/10 * 3/10 * 2/10 * 5/10. = 3/50