1 Alfie has a set of 15 cards numbered consecutively from 1 to 15.
He chooses two of the cards.
- How many different sets of two cards are possible?
Alfie places the two cards side by side to form a number with 2,3 or 4 digits.
- Explain why there are fewer than \({ } ^ { 15 } \mathrm { P } _ { 2 } = 210\) possible numbers that can be made.
- Explain why, with these cards, 1 is the lead digit more often than any other digit.
Alfie makes the number 113, which is a 3-digit prime number.
Alfie says that the problem of working out how many 3-digit prime numbers can be made using two of the cards is a construction problem, because he is trying to find all of them.
- Explain why Alfie is wrong to say this is a construction problem.