Question

Number of three digit of the forms abc such that a<b and c<b is

• A. 285
• B. 240
• C. 260
• D. None of these

Answer 1

Answer: (B)

240

Answer 2

Since, a<b, “a” can take any value from 1, 2, 3, ... b – 1.

Also c < b, “c” can take any value from 0, 1, 2, ...b – 1 ie., “a” can take (b – 1) values, c can take b values. So, under given condition, for any y number of three digit numbers.

= y(y – 1), where y = 2, 3, ..... 9

Required number = $\sum_{y = 2}^{9}{y(y - 1) = \sum_{2}^{9}{y^{2} - \sum_{2}^{9}y}}$

= 285 – 45 = 240