Question

Question 5: Here are four cards.

Each card has a number on it.
7 7
2.
6
4
(a) Write down all the 2-digit numbers that can be made using the cards
(b) Write down all the 3-digit numbers that can be made using the cards

Answer 1

To answer the student's question, there are six unique two-digit numbers (72, 76, 27, 26, 67, 62) and six unique three-digit numbers (726, 762, 276, 267, 627, 672) that can be made using the cards with the digits 7, 7, 2, and 6.

Step-by-step explanation:

The question asks us to determine two-digit and three-digit numbers that can be made using four cards with the digits 7, 7, 2, and 6.

Two-Digit Numbers

For two-digit numbers, we need to pick two different digits and arrange them. Since we have two 7s, they will make the same number regardless of the order, so we should only count them once. The possible two-digit combinations are:

• 72
• 76
• 27
• 26
• 67
• 62

Three-Digit Numbers

For three-digit numbers, we need to pick three different digits and arrange them. As we have duplicate 7s, any combination including both will be the same, thus we only count them once. The possible three-digit combinations are:

• 726
• 762
• 276
• 267
• 627
• 672

Therefore, there are six unique two-digit numbers and six unique three-digit numbers that can be created with the given cards.