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Q.
The number of $4 $ digit numbers without repetition that can be formed by using the digits
$1,2,3,4,5,6,7$ in which each number has two odd digits and two even digits is
Solution:
Two even digits select $^{3} C _{2}$ ways and two odd digits select $^{4}C_{2}$ ways.
$4$ digit numbers can arrange $4 !$ Ways.
Thus, required no.of $4$ digit numbers $=3 C_{2} \times 4 C_{2} \times 4 !=432$