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Standard XI
Mathematics
Fundamental Principle of Counting
How many 3-...
Question
How many
3
-digit even numbers can be formed from the digits
1
,
2
,
3
,
4
,
5
,
6
if the digits can be repeated?
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Solution
A three digit even number is to be formed from given
6
digits
1
,
2
,
3
,
4
,
5
,
6
.
□
□
□
H
T
O
Since, for the number is to be even , so ones place can be filled by
2
,
4
or
6
. So, there are
3
ways to fill ones place.
Since, repetition is allowed , so tens place can also be filled by
6
ways.
Similarly,hundreds place can also be filled by
6
ways.
So, number of ways in which three digit even numbers can be formed from the given digits is
6
×
6
×
3
=
108
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Fundamental Principle of Counting
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