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Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Rearrangement.

The number of 6 digit numbers between 1 and 300000 which are divisible by 4 and are obtained by rearranging the digits of 112233, is

- 1113
- 15
- 53361
- 5082

Rearrangement

Digits

Divisibility

But try the problem first...

Answer: 15.

Source

Suggested Reading

B.Stat Objective Problem 125

Challenges and Thrills of Pre-College Mathematics by University Press

First hint

numbers with tens place and ones place as 12 can be arranged

(2)(3)(2)(1) divided by 2 ways where 2 is repeated =6 ways

Second Hint

numbers with tens place and ones place as 32 can be arranged

(3)(3)(2)(1) divided by 2 ways where 2 is repeated =9 ways

Final Step

that is 9+6 ways = 15 ways.

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