08:27 - 
Basic Mathematics
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Basic Mathematics
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How many 3 digit numbers can be formed by using the digits 2, 3, 5, 6, 7, 9 repetitions not being allowed i) How many of these are less than 400 ? ii) How many of these are even ? iii) How many of these are multiples of 5 ?
There are 6 digit and we require 3
digit number.
This means we have to fill up 3 places
( units, tenths, and hundredths ) by using
6 digits. Units place can be filled up in 6 ways as we can put any one
of the six digit. After this 5 digits are left behind and 10th place
can be filled up in 5 ways and similarly 100th place can be filled
up in 4 ways.
100
10 1
4 5 6
Therefore the number of ways of
filling up the 3 places = 6 x 5 x 4 = 120
We can just write that no. of ways of
filling up 3 places using 6 digits is
i) How many of these are less than 400 ?
i)
Since
the numbers should be less than 400, we
can put either 2 or 3 in the 100’s place. So
the
100’s place can be filled up in 2
ways.
The other 2 places can filled up with
remaining
5 digits means 5 ways.
Therefore number of numbers less than 400 is 40
ii) How many of these
are even ?
i)
In
units place we must have either 2 or 6. so the units place can be filled up in
2 ways and other places in remaining 5 digits means 5 ways.
100
|
10
|
1
|
2 or 6
|
iii) How many of these
are multiples of 5 ?
A multiple of 5 ends with 0 of 5. as 0
is not one of the digits here, we must have 5 only in units place. So, units
place can be filled up in 1 way, and other two places in 5 ways.
100
|
10
|
1
|
5
|
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