12) How many numbers greater than 100 and less than 10 000 may be formed using the digits 2, 3, 4 and 5 if each digit may be used more than once?
ummm Infinite I m not sure
See, the number greater than 100 and less than 1000 will have how many digits in each number??
need at least 3 digits.
use permutations
Not Atleast Exactly 3.. Because if it has 4 then the number will become 1000.. And we have to ding the numbers between 100 and 1000 but not including 100 and 1000.. Getting??
find in place of ding sorry..
the numbers can contain either 3 or 4 digits right?
but four digits can be 2345, 2354, 3245, etc.
still above 100 and under 1000.
not under 1000, its 10000
Oh sorry I interpreted the question wrong.
10000*
Yes.. It can be of 3 and it can be of 4..
So firstly we find for 3 digits number that is : 101 to 999 Now tell me about the hundredths place?? 101 has 1 as its hundredth place.. it can be 2, 3. 4, 5 , 6 , 7 , 8, 9.. But we have to find the numbers containing 2, 3, 4 and 5 So hundredth place can take 2, 3, 4 and 5... 4 ways.. Getting??
so, in case 1: count the number of 3 digit numbers. |dw:1342866076650:dw| each place can take up 4 digits. so, number of possibilities is 4*4*4. in case 2: count the number of 4 digit numbers. |dw:1342866179490:dw| each place can take up 4 digits. so, number of possibilities is 4*4*4*4.
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