How many groups can be selected for playing f | vedclass

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Question

(B) To form two sides (Side $A$ and Side $B$) for a football game,each consisting of one lady and one gentleman:Step $1$: Select one lady and one gent

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(B) To form two sides (Side $A$ and Side $B$) for a football game,each consisting of one lady and one gentleman:Step $1$: Select one lady and one gentleman for Side $A$ from $5$ ladies and $4$ gentlemen.Number of ways $= {}^{5}C_{1} 	imes {}^{4}C_{1} = 5 	imes 4 = 20$ ways.Step $2$: After selecting one lady and one gentleman for Side $A$,we are left with $4$ ladies and $3$ gentlemen.Now,select one lady and one gentleman for Side $B$ from the remaining $4$ ladies and $3$ gentlemen.Number of ways $= {}^{4}C_{1} 	imes {}^{3}C_{1} = 4 	imes 3 = 12$ ways.Step $3$: The total number of ways to form the two sides is the product of the ways to form each side.Total ways $= 20 	imes 12 = 240$.

How many groups can be selected for playing football out of $5$ ladies and $4$ gentlemen such that there should be one lady and one gentleman on each side?

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