Gayatri has forgotten her locker password. But she knows following things

1. The password contain 6 numbers
2. First two numbers are prime numbers and last two numbers are composite numbers.
3. There is at one 0 in the password and there is not a single 1
4. Prime numbers can get repeated but composite number cannot be repeated

Find out the maximum number of attempts she needs to make before finding out correct password

Hi Nikita Tater,
There are 6 numbers in the password.
_, _, _, _, _, _
Prime numbers - 2, 3, 5, 7
Composite numbers - 4, 6, 8, 9
First two numbers are prime and can be repeated; therefore, number of ways = 4*4
Last two numbers are composite and cannot be repeated; therefore, number of ways = 4*3
One number is zero. Other number can be either prime or composite
Case (i): If prime
There are 2 possible positions for 0.
Total number of ways = 4*4*4*3*1*4*2 = 1536
Case (ii): If composite
There are 2 possible positions for 0.
Total number of ways = 4*4*4*3*1*2*2 = 768
Total number of ways = 1536 + 768 = 2304
Hope this helps!

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