Determine the number of 5 card combinations o | vedclass

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(A) In a deck of $52$ cards,there are $4$ aces and $48$ non-ace cards.We need to select $5$ cards such that there is exactly $1$ ace.First,select $1$

Vedclass · Accepted Answer

$778320$

Vedclass · Answer

(A) In a deck of $52$ cards,there are $4$ aces and $48$ non-ace cards.We need to select $5$ cards such that there is exactly $1$ ace.First,select $1$ ace from $4$ available aces in $^{4}C_{1}$ ways.Next,select the remaining $4$ cards from the $48$ non-ace cards in $^{48}C_{4}$ ways.Using the multiplication principle,the total number of combinations is $^{4}C_{1} 	imes ^{48}C_{4}$.$^{4}C_{1} = 4$.$^{48}C_{4} = \frac{48 	imes 47 	imes 46 	imes 45}{4 	imes 3 	imes 2 	imes 1} = 194580$.Total combinations $= 4 	imes 194580 = 778320$.

Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly one ace in each combination.

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