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Find the number of 4-digit numbers that contain exactly two even and two odd digits.

User SajjadG
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Answer:

There are six possible forms of 4-digit numbers consisting of two odd digits and two even digits:

OOEE

OEOE

OEEO

EEOO

EOEO

EOOE

Each of the three forms starting with (O)dd digits can form 5^4 = 625 numbers, since there are 5 odd and 5 even digits.

Each of the three forms starting with (E)ven digits can form 4*5^3 = 500 numbers, since the first digit cannot be zero.

Therefore, the total numbers possible is 3*(625+500)

= 3,375

Explanation:

User MrEs
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