OCR Further Discrete AS 2024 June — Question 3

Exam BoardOCR
ModuleFurther Discrete AS (Further Discrete AS)
Year2024
SessionJune
TopicPermutations & Arrangements
TypeDigit arrangements forming numbers

3 Heidi has a pack of cards.
Each card has a single digit on one side and is blank on the other side.
Each of the digits from 1 to 9 appears on exactly four cards.
Apart from the numerical values of the digits, the cards are indistinguishable from each other.
Heidi draws four cards from the pack, at random and without replacement. She places the four cards in a row to make a four-digit number. Determine how many different four-digit numbers Heidi could have made in each of the following cases.
  1. The four digits are all different.
  2. Two of the digits are the same and the other two digits are different.
  3. There is no restriction on whether any of the digits are the same or not.