I only need part c in the image provided. **Bridge: Understanding Card Distributions**In the game of Bridge, a hand consists of an unordered arrangement of 13 cards dealt randomly from a standard deck of 52 playing cards. Let's explore some related problems:**a. How many possible bridge hands are there?**To find the number of possible bridge hands, we calculate the combinations of 13 cards that can be drawn from a deck of 52 cards.**b. What is the probability of being dealt a bridge hand that contains exactly two of the four aces?**This involves calculating the combinations of selecting 2 aces from 4 and the remaining 11 cards from the 48 non-ace cards.**c. Find the probability of being dealt an 8-4-1 distribution.**In this scenario, we are asked to find the probability of receiving 8 cards of one suit, 4 of another, and 1 of a third suit. This distribution requires careful calculation of combinations for each scenario.**Note:**In the spreadsheet image, part "a" is highlighted in yellow with the number "[4]" indicating a placeholder or part of the calculation for one of the problems (not accurate for total bridge hands). Part "c" is unfilled, suggesting further work is needed there.

Answered: c. Find the probability of being dealt…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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I only need part c in the image provided.

**Bridge: Understanding Card Distributions**

In the game of Bridge, a hand consists of an unordered arrangement of 13 cards dealt randomly from a standard deck of 52 playing cards. Let's explore some related problems:

**a. How many possible bridge hands are there?**

To find the number of possible bridge hands, we calculate the combinations of 13 cards that can be drawn from a deck of 52 cards.

**b. What is the probability of being dealt a bridge hand that contains exactly two of the four aces?**

This involves calculating the combinations of selecting 2 aces from 4 and the remaining 11 cards from the 48 non-ace cards.

**c. Find the probability of being dealt an 8-4-1 distribution.**

In this scenario, we are asked to find the probability of receiving 8 cards of one suit, 4 of another, and 1 of a third suit. This distribution requires careful calculation of combinations for each scenario.

**Note:**

In the spreadsheet image, part "a" is highlighted in yellow with the number "[4]" indicating a placeholder or part of the calculation for one of the problems (not accurate for total bridge hands). Part "c" is unfilled, suggesting further work is needed there.

Expert Solution

Step 1

There are 52 cards in standard deck in which there are 4 types of suits with 13 cards in each suit.

The number of possible ways that a delta (13-cards) are selected from 52 cards is $(\begin{matrix} 52 \\ 13 \end{matrix})$ ways. The number of ways that 8 cards are selected from one suit is $(\begin{matrix} 13 \\ 8 \end{matrix})$ ways. The number of ways that 4 cards are selected from another suit is $(\begin{matrix} 13 \\ 4 \end{matrix})$ ways, and the number of ways that 1 card is selected from another suit is $(\begin{matrix} 13 \\ 2 \end{matrix})$ ways.

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