Question

How many 5 digit numbers formed using the digits 0,1,2,3,4,5 divisible by 5 if digits are not repeated

Please give explanation

Class 11 Permutations​

Answer 1

Answer:

9

Step-by-step explanation:

five digit no formed by 0 1 2 3 4 5=10 20 30 40 50 21 23 24 25 31 32 34 35 41 42 43 45 51 52 53 54 12 13 14 15

no divisible by 5=10 20 30 40 50 15 25 35 45

Answer 2

Answer:

216

Step-by-step explanation:

The numbers are divisible by 5 if they end with either 0 or 5.

(i)

Let the number ends with 0 i.e. unit's digit is 0.

Then, There are 5 choices for ten's place.

Now,

As the repetition is not allowed,

=> 4 choices for hundred' place,

=> 3 choices for thousand's place and

=> 2 choices for the first digit.

So,

The 5 digits numbers that can be formed which ends with 0 and 5 is :

5 * 4 * 3 * 2 = 120 .

(ii)

Let the number ends with 5 i.e. unit's digit is 5.

Now,

As the repetition is not allowed,

=> 4 choices for hundred' place.

=> 3 choices for thousand's place, and

=> 2 choices for the first digit.

So,

The 5 digits numbers that can be formed which ends with 5 = 5 * 4 * 3 * 2 = 120.

But,

The first digit can't be 0. So,

We need to subtract that numbers which contains 0 as first digit.

If 0 is the first digit, then number of places left to be filled is 4 and that can be done in 4! ways.

So, the 5 digits numbers that can be formed which ends with is 120 - 4! = 96.

Thus,

Total number of five digit numbers divisible by 5 is 120 + 96 = 216

Hope it helps!