Question

Using all the first five natural numbers,

(i) how many numbers can be formed?
(ii) how many numbers greater than 30,000 can be formed?
(iii) how many numbers divisible by 5 can be formed?

Answer 1

First five natural numbers are 1 2 3 4 5

(i) Total numbers can be formed = ⁵P₅

= 5!

= 120

(ii) For the numbers greater than 30,000, the digit at the first place can by any one of the digits 3, 4, 5 and remaining 4 places can be arranged from the remaining 4 digits.

.-. Total permutations = ³P₁ × ⁴P₄

= 3 × 4!

= 3 × 24

= 72

(iii) For the number divisible by 5, the last digit in the humber should be 5. Remaining 4 places can be arranged from the remaining 4 digits accept digit 5.

∴ Total permutations = ¹P₁ × ⁴P₄

= 1 × 4!

= 1 × 24 = 24