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klio [65]
4 years ago
7

A flush in a five-card poker hand is five cards of the same suit. The suits are spades, clubs, diamonds and hearts. How many spa

de flushes are possible in a 52-card deck? How many flushes are possible in any suit?
Business
1 answer:
padilas [110]4 years ago
8 0

Answer:

1287 spade flushes possible in a 52-card deck.

1287 flushes in any suit.

Explanation:

We have been given that a flush in a five-card poker hand is five cards of the same suit. The suits are spades, clubs, diamonds and hearts.

To find the number of possible spade flushes in a 52-card deck, we need to find choosing 5 cards from 13 cards as a standard deck has 13 spades altogether.

^{13}C_5=\frac{13!}{5!(13-5)!}

^{13}C_5=\frac{13!}{5!(8)!}\\\\^{13}C_5=\frac{13*12*11*10*9*8!}{5*4*3*2*1(8)!}

^{13}C_5=13*11*9\\\\^{13}C_5=1287

Therefore, there are 1287 spade flushes possible in a 52-card deck.

Since there 1287 possible suits in spade flushes and flushes of different suits are mutually exclusive events, therefore, there will be 1287 flushes in any suit.

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This year, Randy paid $30,250 of interest on his residence. (Randy borrowed $480,000 to buy his residence, and it is currently w
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Answer:

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Explanation:

Randy can deduct $33,050 i.e. (30,250 + 2800)

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4 years ago
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