A man X has 7 friends, 4&nb | vedclass

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Question

$X 	o 4$ ladied               $Y 	o 3$

$X 	o 3$ men              &nbs

Vedclass · Accepted Answer

$485$

Vedclass · Answer

$X 	o 4$ ladied               $Y 	o 3$

$X 	o 3$ men               $Y 	o 4$

Possible cases for $X$ are

$(1)$ $3$ ladies, $0$ man

$(2)$ $2$ ladies, $1$ man

$(3)$ $1$ lady, $2$ men

$(4)$ $0$ ladies, $3$ men

Possible cases for $Y$ are

$(1)$ $0$ ladies, $3$ men

$(2)$ $1$ ladies, $2$ men

$(3)$ $2$ lady, $1$ man

$(4)$ $3$ ladies, $0$ man

No. of ways ${ = ^4}{C_3}{ \cdot ^4}{C_3} + {{(^4}{C_2}{ \cdot ^3}{C_1})^2} + {{(^4}{C_1}{ \cdot ^3}{C_2})^2} + {{(^3}{C_3})^2}$

$ = 16 + 324 + 144 + 1 = 485$

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