Question

We call a number a descending number if each digit is strictly smaller than the digit that comes before it. For example, $863$ is a descending number. How many $3$-digit descending numbers are there

Answer 1

There are 120 of 3-digit descending numbers in total.

There is just one three-digit number that is a falling number if 2 is in the hundreds position, and that number is 210.

There are three such descending numbers if the number three is in the hundreds location.

310

320

321

Six descending numbers are available if 4 is in the hundreds place.

410

420

421

430

431

432

We have 10 descending numbers if the number five is in the hundreds location.

510

520

521

530

531

532

540

541

542

543

The current totals are: 1, 3, 6, and 10.

A +2 jump occurs from 1 to 3.

There is a +3 jump from 3 to 6.

From 6 to 10, there is a +4 jump.

Since there are 15 descending numbers and 6 is the hundreds digit, they are as follows: 610 620 621 630 631 632 640 641 642 643 650 651 652 653 654

Also included are the descending numbers 15+6 = 21 with the hundreds digit 7; 21+7 = 28 with the hundreds digit 8; and 28+8 = 36 with the hundreds digit 9.

They are 1,3,6,10,15,21,28, and 36.

1+3+6+10+15+21+28+36.

Equals 120 when added together.

Thus, there are 120 of 3-digit descending numbers in total.

Learn more about descending numbers at

brainly.com/question/13193576

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