neerajkumar1_1 wrote:How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?
20
150
225
300
320
Good = total - bad.
Total:
The thousands digit must be 2, 4, 6 or 8:
Number of options = 4.
The hundreds digit must be 1, 3, 5, 7, or 9:
Number of options = 5.
The tens digit must be 2, 3, 5, or 7:
Number of options = 4.
The units digit must be 0, 3, 6, or 9:
Number of options = 4.
To combine these options, we multiply:
4*5*4*4 = 320.
Bad:
A bad integer has a thousands digit and a tens digit both equal to 2.
As seen above:
Number of options for the hundreds digit = 5.
Number of options for the units digit = 4.
To combine these options, we multiply:
5*4 = 20.
Good = 320-20 = 300.
The correct answer is
D.
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