CAT 1998 — QA Question 9
âââââââDirection: Answer the questions based on the following information.
Production pattern for number of units (in cubic feet) per day.
For a truck that can carry 2,000 cubic ft, hiring cost per day is Rs. 1,000. Storing cost per cubic feet is Rs. 5 per day.
How many numbers can be formed from 1, 2, 3, 4, 5, without repetition, when the digit at the unit’s place must be greater than that in the ten’s place?
Answer & solution
- A
54
60
- C
17
- D
2 × 4!
u > t
Case (i): t = 1
u can be 2, 3, 4, 5 ⇒ 4 possibilities
So total possible number that can be formed
= 4 × 3 × 2 × 1
Case (ii): t = 2
u can be 3, 4, 5 ⇒ 3 possibilities
So total possible number that can be formed
= 3 × 3 × 2 × 1
Case (iii): t = 3
u can be 4, 5 ⇒ 2 possibilities
So total possible number that can be formed
= 2 × 3 × 2 × 1
Case (iv): t = 4
u can be 5 ⇒ 1 possibility
So total possible number that can be formed
= 1 × 3 × 2 × 1
Hence, total possible number = (4 + 3 + 2 + 1) = 60