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Determine the Number of 5 Cards Combinations Out of a Deck of 52 Cards If at Least One of the 5 Cards Has to Be a King? - Mathematics

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Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?

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Solution

There are 4 kings in the deck of cards.
So, we are left with 48 cards out of 52.
∴ Required combination =\[{}^{48} C_1 \times^4 C_4 + {}^{48} C_2 \times^4 C_3 + {}^{48} C_3 \times^4 C_2 + {}^{48} C_4 \times^4 C_1 \]

\[= 48 + 4512 + 103776 + 778320\]
\[ = 886656\]

Concept: Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 22 | Page 16

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