CAT 1998 — QA Question 9

$\frac{}{} \frac{}{} \frac{}{} \frac{t}{Ten\text{'}s place} \frac{u}{Unit\text{'}s place}$

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) $\overline{)\underline{3}}$ = 60