Question

Find the number of 4-digit numbers greater than 3000 that can be formed from prime numbers from 1 to 10 without repetitions. ( Can't solve by listing out the possible outcomes without calculations )?

Answer 1

18

Explanation:

Let's first note that the prime numbers between 1 and 10 is:

2, 3, 5, 7

1 is not prime (see here as to why).

We want 4 digit numbers that are greater than 3000, which means we can't start with the 2. And so there are 3 numbers that can be in the first position (3, 5, 7).

In the following 3 positions, there are 3 numbers to place in there, which can be done `3!` ways.

All told then, we have `3xx3! = 3xx6 = 18`