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Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > Determine the number of 5 cards combinations out of...
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Determine the number of 5 cards combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

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a) the total cards = 52 and sequence of 5 cards and there 4 queen in the standard deck. There for 52^4 x 51 x 50 x 4 choices b) total cards = 52 ^5 - 8x7x6x5x4x3x2x1 choices
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1 king can be chosen in 4C1 ways = 4 out of remaining 48 cards 4 can be chosen in 48C4 ways = 194580 ways. Total = 778320 ways
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SME in Mathematics & Statistics

There are 4 kings in a deck of 52 cards. 1 king can be chosen in 4C1 ways. Once this selection is made, then out of the remaining 52 - 4 = 48 cards, 4 cards cab be chosen in 48C4 ways. Hence, the answer is (4C1)(48C4).
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Learn Mathematics with me in fun

4C1 * 48C4
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Learn Mathematics with me in fun

4C1 multiplied by 48C4
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4C1 multiplied by 48C4
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Excellent in Chemistry(For IIT & Medical aspirants) & 7 year of Exp. in Byju, Nucleus,Sarvottam(Kota

For exactly 1 king there is (4c1) ways and for another 4 cards i have (48c4) ways so total ways are (4c1)(48c4).I hope it will help u.
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GMAT Math Expert

(4C1)*(48C4), where 4C1 is to chose 1 King out of 4 Kings and once a king is selected from the remaining 48 cards, we can select 4 other cards in 48C4 ways.
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