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Byju's Answer
Standard VI
Mathematics
How Many Numbers Can Be Formed Using a Certain Number of Digits?
how many numb...
Question
how many numbers greater than 300 but less than 3000 can be formed using the digits 0,1,2,3,4,5 if repetition is not allowed
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Solution
Consider
the
3
-
digit
numbers
at
first
.
Now
,
the
hundreds
place
can
be
filled
with
any
one
of
3
numbers
3
,
4
or
5
.
Number
of
ways
to
fill
hundreds
place
=
3
Now
,
number
of
ways
to
fill
tens
place
=
5
Number
of
ways
to
fill
ones
place
=
4
So
,
total
number
of
3
digit
numbers
=
3
×
5
×
4
=
60
Consider
the
4
-
digit
numbers
.
Now
,
the
thousands
place
can
be
filled
by
either
1
or
2
.
Number
of
ways
to
fill
thousands
place
=
2
Number
of
ways
to
fill
hundreds
place
=
5
Now
,
number
of
ways
to
fill
tens
place
=
4
Now
,
number
of
ways
to
fill
ones
place
=
3
So
,
total
number
of
4
-
digit
numbers
=
2
×
5
×
4
×
3
=
120
Hence
,
total
number
of
required
numbers
=
60
+
120
=
180
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