Bunuel wrote:
How many 4-digit positive integers are there in which half of the digits are even and another half of the digit is odd?
A. 625
B. 1,125
C. 1,250
D. 9,000
E. 10,000
Case 1: When Thousands place is EvenThousands place can be filled in 4 ways using digits 2, 4, 6, 8
One more place for even digit can be chosen in 3 ways and may be filled in 5 ways using digits 0, 2, 4, 6, 8
other two places may be filled in 5*5 ways using digits 1, 3, 5, 7, 9
i.e. Total Outcomes = 4*3*5*5*5 = 1500
Case 2: When Thousands place is ODDThousands place can be filled in 5 ways using digits 1, 3, 5, 7, 9
two places for even digits may be chosen in 3C2 = 3 ways and may be filled in 5*5 ways using digits 0, 2, 4, 6, 8
remaining place may be filled in 5 ways using digits 1, 3, 5, 7, 9
i.e. Total Outcomes = 5*3*5*5*5 = 1875
Total Such numbers = 1500+1875 = 3375
Bunuel Answer Options should be adjusted accordingly...
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