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The number of \( 4 \) digit numbers without repetition that can be formed using the digits \( 1,2,3,4 \),
\( 5,6,7 \) in which each number has two odd digits and two even digits is
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\( 5,6,7 \) in which each number has two odd digits and two even digits is
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The correct answer is:
\( 432 \)
(C)
Given digits are \( 1,2,3,4,5,6,7 \).
Two even digits can be selected in \( { }^{3} C_{2} \)
Two odd digits can be selected in \( { }^{4} C_{2} \) ways.
These selected \( 4 \) digits can be arranged in \( 4 ! \) ways.
\( \therefore \) Total number of ways \( ={ }^{4} C_{2}{ }^{3} C_{2}{ }_{2} ! \)
\( =6 \times 3 \times 24 \)
\( =18 \times 24 \)
\( =432 \)
Given digits are \( 1,2,3,4,5,6,7 \).
Two even digits can be selected in \( { }^{3} C_{2} \)
Two odd digits can be selected in \( { }^{4} C_{2} \) ways.
These selected \( 4 \) digits can be arranged in \( 4 ! \) ways.
\( \therefore \) Total number of ways \( ={ }^{4} C_{2}{ }^{3} C_{2}{ }_{2} ! \)
\( =6 \times 3 \times 24 \)
\( =18 \times 24 \)
\( =432 \)
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