Question

c) Make two 4-dight numbers using each of the digits 1, 2, 4, and 5 such that the
numbers made are divisible by 132.
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Answer 1

Answer:

Let four digit number — — — —

We know that number is divisible by 4 if it's last two digit are divisible by 4.

So it's unit digit can be 2 or 4 because if unit digit is any of odd number than it is not divisible by 4.

We have two cases:-

1)if reputation of digit allowed:-

Then if unit digit is 2 then we can fill tenth digit with 1 ,3,5 means we have 3 options so

total number=5*5*3*1=75

If unit digit is 4 then we can fill tenth digit with

2 and 4 so we have two option so

Total number=5*5*2*1=50

Both case have or so we add both

Answer=75+50=125

2) )if reputation of digit not allowed:-

Then if unit digit is 2 then we can fill tenth digit with 1 ,3,5 means we have 3 options , hundred digit with 3 options and thousand digit with 2options so

total number=2*3*3*1=18

If unit digit is 4 then we can fill tenth digit with only Two so one options ,hundred digit with remaining 3 options and thousand digit with two option so

Total number=2*3*1*1=6

Both case have or so we add both

Answer=18+6=24

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