Mathematics 9709 · AS & A Level · Permutations and combinations
Permutations and combinations — practice question
A security code is made up of 2 letters, then a 4-digit number. The letters come from $\{A, B, C, D, E\}$ and the digits come from $\{1, 2, 3, 4, 5, 6, 7\}$. No letter or digit can be used more than once. One example of such a code is BE3216.
(a)[2]
In how many different ways can the codes be formed?
(b)[3]
Determine how many different codes contain the letter $A$ or the digit $5$ or both.
(c)[3]
A security code is generated at random. Find the probability that the code is $DE$ followed by a number between $4500$ and $5000$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct permutation method, for example $^5P_2\times{}^7P_4$ or an equivalent product.” …