Question

Pick two or fewer different digits from the set {1, 3, 6, 7} and arrange them to form a number. How many prime numbers can we create in this manner

Answer 1

3,7,13,17,31,37,61,67,71,73

Answer 2

Answer:

Step-by-step explanation:

We have two cases: the number is either 1-digit or 2-digit. We examine each of these cases separately.

Case 1: 1 digit

In this case, the only 1-digit primes are 3 and 7, for a total of 2 primes.

Case 2: 2 digits

We have the following combinations of numbers: 13, 16, 17, 36, 37, 67, 76, 73, 63, 71, 61, 31. Out of these 12 numbers, it is easier to count the composites: 16, 36, 76, and 63 for a total of 4 composites, which we subtract from the original 12 numbers to yield $12-4=8$ primes in this case.

Both cases considered, the total number of prime numbers we can create is $2 + 8 = \boxed{10}$.