Explanatory Answer

Method of solving this CAT Quantitative Ability Question from Permutation, Combination and Probability question

(b) The numbers should be formed from 1, 2, 3, 4 and 5 (without repetition), such that the digit at the units place must be greater than in the tenth place.

Tenth place has five options. If 5 is at the tenth place then the digit at the unit’s place cannot be filled by the digit greater than that at the tenth place.

If 4 is at the tenth place, then the unit’s place has only option of 5, while the three places can be filled up in 3! Ways.

If 3 is at the tenth place, then the units’ place can be filled up by 4 or 5, i.e. in 2 ways.

While other three places can filled up in 3! ways. If 2 is at the tenth place, then the unit’s place can be filled up by 3, 4 or 5 i.e. in 3 ways.

While other three places can be filled up in 3! Ways. If 1 is at the tenth place, then any other four places can be filled up in 4! Ways.

Thus the total number of numbers satisfying the given conditions is 0 + 3! + 2(3!) + 3(3!) + 4! = 60.