Descending deal
Four cards from a set numbered 1-36 are dealt. What is the probability that they are dealt in order?
Age
14 to 16
Challenge level
Problem
The cards in a set of $36$ are numbered $1$ to $36$.
The cards are shuffled and four cards are dealt.
What are the chances of them being dealt in descending order?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
The number of different arrangments of the four cards which are dealt is $4\times 3\times2\times1 = 24$.
In only one of these will the four cards be in descending order, hence the probability is $\frac1{24}$.