Find the number of ways,the digits 0,1,2,3 can be permuted to give rise to a number greater than 2000.
clearly, the first digit must be 2 or 3
Once that is chosen, you have 3 digits left, so
2*3!
John
To find the number of ways the digits 0, 1, 2, 3 can be permuted to give a number greater than 2000, we need to consider a few conditions:
1. The first digit cannot be 0: Since the number must be greater than 2000, the first digit cannot be 0. This leaves us with 3 options: 1, 2, and 3.
2. The second digit can be any of the remaining three digits: After choosing the first digit, any of the remaining three digits can be used as the second digit.
3. The third digit can be any of the remaining two digits: After choosing the first and second digits, any of the remaining two digits can be used as the third digit.
4. The fourth digit can be any of the remaining one digit: After choosing the first three digits, there is only one remaining digit left.
To find the total number of ways, we multiply the number of choices at each step:
Total number of ways = Number of choices for the first digit × Number of choices for the second digit × Number of choices for the third digit × Number of choices for the fourth digit
Number of choices for the first digit = 3 (since it cannot be 0)
Number of choices for the second digit = 3 (any of the remaining three digits)
Number of choices for the third digit = 2 (any of the remaining two digits)
Number of choices for the fourth digit = 1 (the remaining digit)
Total number of ways = 3 × 3 × 2 × 1 = 18
Therefore, there are 18 different ways the digits 0, 1, 2, 3 can be permuted to give a number greater than 2000.