Question

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Answer 1

Hey there!!

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The correct answer is

Answer=D

Answer : Option D

Explanation :

Initially we will find out the number of 8 digits mobile numbers that can be formed if

any digit can be repeated (with 0 can also start the mobile number)

The digits can be repeated and 0 can also be used to start the mobile number.

Hence, any of the 10 digits(0,1,2,3,4,5,6,7,8,9) can be placed at any place of

the 8 digit number

10 10 10 10 10 10 10 10

Hence, the total number of 8 digit mobile numbers that can be formed using all

the digits (0,1,2,3,4,5,6,7,8,9) if any digit can be repeated (with 0 can also

start the mobile number) = 108 ---(A)

Now we will find out the number of 8 digits mobile numbers that can be formed

if no digit can be repeated (with 0 can also start the mobile number)

In this case, any of the 10 digits can be placed at the 1st position.

Since one digit is placed at the 1st position, any of the remaining

9 digits can be placed at 2nd position.

Since 1 digit is placed at the 1st position and another digit is placed

at the 2nd position, any of the remaining 8 digits can be placed at the

3rd position.

So on …

10 9 8 7 6 5 4 3

i.e., the number of 8 digits mobile numbers that can be formed if no digit can be

repeated (with 0 can also start the mobile number)

= 10P8 ---(B)

(In fact you should directly get (A) and (B) without any calculations

from the definition of permutations itself)

From(A) and (B),

the number of 8 digits mobile numbers that can be formed if at least one of their digits

is repeated and 0 can also start the mobile number

= 108 - 10P8

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