Question

Find the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.​

Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

Find the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

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$\Large\fbox{\color{purple}{ SOLUTION }}$

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➡️Take a deck of 52 cards,

➡️To get exactly one king, 5-card combinations have to be made.

➡️It should be made in such a way that in each selection of 5 cards, or in a deck of 52 cards, there will be 4 kings.

➡️To select 1 king out of 4 kings = 4^c1

➡️To select 4 cards out of the remaining 48 cards = 48^c4

➡️To get the needed number of 5 card combination = 4^c1 x 48^c4

➡️= 4x2x 47x 46×45

➡️= 778320 ways

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Answer 2

Answer:

➡ SOLUTION :-

➡️Take a deck of 52 cards,

➡️To get exactly one king, 5-card combinations have to be made.

➡️It should be made in such a way that in each selection of 5 cards, or in a deck of 52 cards, there will be 4 kings.

➡️To select 1 king out of 4 kings = 4^c1

➡️To select 4 cards out of the remaining 48 cards = 48^c4

➡️To get the needed number of 5 card combination = 4^c1 x 48^c4

➡️= 4x2x 47x 46×45

➡️= 778320 ways ✔✔

Step-by-step explanation:

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