Question

How many four-digit numbers can be formed using the digits 1, 2, 3, 5, 8 if repetition of
digits is not allowed ? How many of these are
(i)divisible by 3
(ii)divisible by 5
(Oct. 2008)
(iii) odd
(iv) between 2000 and 5000 ?
step by step explanation please​

Answer 1

Answer:

11,12,13,15,18,21,23,25,28,31,32,33,35,38,51,52,53,58,81,82,83,85

(1) 12,15,18,21,38,52,58

(2)15,25,35,85

Step-by-step explanation:

I hope it's helpful to U

Answer 2

Answer:

There can be total 120 four digit numbers formed by using the digits 1, 2, 3, 5, 8 if repetition of digits is not allowed.

Step-by-step explanation:

There are 5 digits.

As repetition of digits is not allowed,  then

• One's place can be written using 5 digits.
• Ten's place can be written using 4 digits.
• Hundred's place can be written using 3 digits.
• Thousand's place can be written using 2 digits.

Therefore, total number of four digit numbers is given by

5 × 4 × 3 × 2 = 120

(i) In order to be divisible by 3, the sum of digits of the numbers must be divisible by 3.

• Digits used are 2, 3, 5 and 8.
• Then sum of digits are  2 + 3 + 5 + 8 = 18
• So, number of four digit numbers divisible by 3 is given by

        4 × 3 × 2 × 1 = 24

(ii) A number is divisible by 5 if digit at one's place is 5.

• One's place can be written using only one digit 5.
• Ten's place is written using 4 digits.

• Hundred's place is written using 3 digits.
• Thousand's place is written using 2 digits.

• Hence, number of 4 digit numbers divisible by 5 is given by

      1 × 4 × 3 × 2 = 24

(iii) A number is odd if digit at one's place is either 1 or 3 or 5.

• One's place is written using 3 digits.
• Ten's place is written using 4.
• Hundred's place is written using 3 digits.
• Thousand's place is written using 2 digits.

∴ Number of 4 digit numbers which are odd given by

3 × 4 × 3 × 2 = 72

(iv) Four - digit numbers are between 2000 and 5000 if

• Thousand's place is taken by digit 2 or 3.

• Hundred's place is written using 4 digits.
• Ten's place is written using 3  digits.
• One's place is written using 2 digits.

∴ Required answer = 2 × 4 × 3 × 2 = 48