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Q.

How many $3 -$ digit numbers can be formed by using the digits 0,1,3,5,7 while each

digit may be repeated any number of times?

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a

110

b

90

c

100

d

30

answer is C.

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Detailed Solution

Given,
The digits = 0, 1,3,5,7
Total number of digits = 5
Repetition is allowed
Now, we have to formed 3-digit numbers
In the 1st condition we have
The zero doesn’t contain on hundred’s place.
Thus, we can fill the any digits of

1, 3, 5, 7

Therefore 4 ways to fill it
In the 2nd condition we have
Any out of 5 digits are used to filled on the ten’s place.
Therefore 5 ways to fill it
In the 3rd condition we have
Using any of 5 digits to filled on the place.
Therefore the 5 ways to fill it
Total ways

= (4 \times 5 \times 5)

= 100

Hence the required value is 100.
Correct option is 3.

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