Question

How many three digit numbers not ending with 0 can be formed such that the middle digit is bigger than the extreme digits?

Answer 1

Answer :

We know three digits number can be between 100 - 999
And by conditions our number is like xy0 ( Where y > x )

So in between 100 to 199
we get numbers that can satisfied the given conditions
= 120 , 130 , 140 , 150 , 160 , 170 , 180 , 190 = 8 numbers ( Here we can see that middle term > extreme term )

In between 200 to 299
= 230 , 240 , 250 , 260 , 270 , 280 , 290 = 7 numbers

In between 300 to 399
= 340 , 350, 360 , 370 , 380, 390 = 6 numbers

In between 400 to 499
= 450 , 460 , 470 , 480, 490 = 5 numbers

In between 500 to 599
= 560 , 570 , 580 , 590 = 4 numbers

In between 600 to 699
= 670 , 680 , 690 = 3 numbers

In between 700 to 799
= 780 , 790 = 2 numbers

In between 800 to 899
= 890 = 1 number

In between 900 to 999
= 0 numbers

SO , Total numbers that satisfied given condition will be
= 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0

= 36 ( Ans )