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# Determine the Number of 5-card Combinations Out of a Deck of 52 Cards If Each Selection of 5 Cards Has Exactly One King. - CBSE (Arts) Class 11 - Mathematics

ConceptConcept of Combinations

#### Question

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

#### Solution

From a deck of 52 cards, 5-card combinations have to be made in such a way that in each selection of 5 cards, there is exactly one king.

In a deck of 52 cards, there are 4 kings.

1 king can be selected out of 4 kings in ""^4C_1 ways.

4 cards out of the remaining 48 cards can be selected in ""^48C_4 ways.

Thus, the required number of 5-card combinations is ""^4C_1 xx ""^48C_4

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 7: Permutations and Combinations
Q: 8 | Page no. 157

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Solution Determine the Number of 5-card Combinations Out of a Deck of 52 Cards If Each Selection of 5 Cards Has Exactly One King. Concept: Concept of Combinations.
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