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  4. There are 3 men and 7 women taking a dance class. Number of different ways in which each man be paired with a woman partner, and the four remaining women be paired into two pairs each of two, is

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Q. There are 3 men and 7 women taking a dance class. Number of different ways in which each man be paired with a woman partner, and the four remaining women be paired into two pairs each of two, is

Permutations and Combinations

Solution:

image 3 women can be selected in ${ }^7 C _3$ ways and can be paired with 3 men in 3 ! ways.
Remaining 4 women can be grouped into two couples in $\frac{4 !}{2 ! \cdot 2 ! \cdot 2 !}=3$
$\therefore $ total $={ }^7 C _3 \cdot 3 ! \cdot 3=630$