Question

How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ?

Answer 1

Answer:

49

Step-by-step explanation:

The "abc" be the number between 100 and 299

So, we can say:

0<a<b<c<9  [from the constraints]

c can take values from 3 - 9 inclusive, so that's 7 values

b can take values from 2 - 8, inclusive, so that's 7 values

a can take only 1 value

So the number of possibilities is:

7 * 7 * 1 = 49

Hence, there are 49 integers between 100 and 299 such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n