Question

numbers such as 543 or 531 have their digts in decreasing order beacuse each digit is less than the digit to its left. the digit in 322 are not in decreasing order. how many whole nmbers between 100 and 599 have their digit in decreasing order.

Answer 1

The numbers are - 210 , 310, 320, 321, 410, 420, 421, 430, 431, 432, 543, 542, 541, 540, 532, 531, 530, 521, 520, 510  

Explanation:

To find the number between 100 and 599 that have their digit in decreasing order, we can use combination method. The first digit cannot be 1, because there are no descending options for the following digits.

If the first digit is 2, then the only possibility is 210.

If the first is 3, the numbers can be 310, 320, and 321.

If the first is 4, they can be 432, 431, 430, 421, 420, 410

If the first is 5, they can be 543, 542, 541, 540, 532, 531, 530, 521, 520, 510

Therefore, there are 20 numbers that satisfies the rule.

The numbers are - 210 , 310, 320, 321, 410, 420, 421, 430, 431, 432, 543, 542, 541, 540, 532, 531, 530, 521, 520, 510