Question

4) Sandeep, Hee, Sara, and Mohammad play euchre with a standard deck consisting of 24 cards (A, K, Q, J, 10, and 9 from each of the four suits of a regular deck of playing cards). In how many ways can the deck be dealt so that each player receives 5 cards, with 4 cards left in the middle, one of which is turned face-up

Answer 1

Answer:

1.19685 × 10¹⁶

Step-by-step explanation:

From the given information.

Since each players receives 5 cards; then = 5 * 4 = 20

Now, the process to go about this is to first select 5 cards out of 24 that goes to player 1. Then from the remaining 19, we can select another 5 cards that goes to player 2, etc. until 4 cards are left, out of which one is remained faced up. Thus, the 4 sets of 5 cards selected can be shuffled in 4! ways.

∴

No fo ways = $^{24}C_5 \times ^{19}C_5 \times ^{14}C_5 \times ^{9}C_5 \times 4! \times ^{4}C_1$

$= \dfrac{24!}{5!(24-5)!}\times \dfrac{19!}{5!(19-5)!}\times \dfrac{14!}{5!(14-5)!}\times \dfrac{9!}{5!4!}\times 4! \times \ \dfrac{4!}{1!(4-1)!}$

$= \dfrac{24!}{5!^4}\times 4$

= 1.19685 × 10¹⁶