How many numbers can be formed from 1, 2, 3, 4, 5(without repeating), where the digit at the unit’s place must be greater than that in the ten’s place?(CAT 1998)

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Solution

The correct option is B 60
Option (b)
Case 1- units place= 1 (0 possibilities)
Case 2- units place = 2 (tens place=1 possibility (2) and 3! Arrangements for the remaining places) = 1x3!
Case 3- units place = 3 (tens place=2 possibilities (1,2) and 3! Arrangements for the remaining places) = 2x3!
Case 4- units place = 4 (tens place=3 possibilities (1,2,3) and 3! Arrangements for the remaining places) = 3x3!
Case 5- units place = 5 (tens place=4 possibilities (1,2,3,4) and 3! Arrangements for the remaining places) = 4x3!
Total = 60

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