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Brums [2.3K]
3 years ago
6

How many ways are there to select a 5-card hand from a regular deck such that the hand contains at least one card from each suit

. Recall that a regular deck has 4 suits, and there are 13 cards of each suit for a total of 52 cards. Hint: Use Inclusion-Exclusion principle.
Mathematics
1 answer:
Snezhnost [94]3 years ago
6 0

Answer:

There are 685464 ways of selecting the 5-card hand

Step-by-step explanation:

Since the hand has 5 cards and there should be at least 1 card for each suit, then there should be 3 suits that appear once in the hand, and one suit that apperas twice.

In order to create a possible hand, first we select the suit that will appear twice. There are 4 possibilities for this. For that suit, we select the 2 cards that appear with the respective suit. Since there are 13 cards for each suit, then we have {13 \choose 2} = 78 possibilities. Then we pick one card of all remaining 3 suits. We have 13 ways to pick a card in each case.

This gives us a total of 4*78*13³ = 685464 possibilities to select the hand.

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What is y=x 9x-2y=-49 using substitution
Veronika [31]

Answer:

y= -7

Step-by-step explanation:

Substitute y for x in the equation since the rule is true.

6 0
2 years ago
Bruce drove 25 km and his car used 4 L of gas. How many km can Bruce drive with 30 L of gas? Round your answer to the nearest km
Rudik [331]

Answer:

188km

Hi there!!

I hope this answer helps.

Step-by-step explanation:

You can solve this with simple cross multiplication. (proportion)

Step-by-step explanation:

7 0
2 years ago
Factorise -75ab² - 15ac
Verdich [7]

Answer:

1)  -15·a·(5·b² + c)

2) h < 4

3) 4·x² - 9

4) 1792

5)  156°

6) 2t cm

7) 2·a·m·(2·m - 3)

8)  10 cm

9) 0.00051

10)  #47,250

11)  -10·p·q

12) 1.35 × 10⁻⁴

13) 320°

14) 20 cm

15) 12·x²·y²

16) 6.36 × 10⁵

17) 4 cm

18)  225°

19) 1034 cm²

20) 29

Step-by-step explanation:

1) The given expression is -75·a·b - 15·a·c

Which can be expressed as -15·a·(5·b² + c)

2) The height, h < 2 × 12/6 = 4

h < 4

3) (2·x - 3)·(2·x + 3) = 4·x² - 9

4) The selling price = 1.12 × 200 × 8 = 1792

5) The interior angle of a polygon is given by the relation;

(n - 2)×180/n for 15, we get;

(15 - 2)×180/15 = 156°

6) 2t cm

7) 4·a·m² - 6·a·m = 2·a·m·(2·m - 3)

8) Slant height = √(8² + 6²) = 10 cm

9) 51 × 10⁻⁵ = 0.00051

10) Cash price = #54,000 × (1 - 0.125) = #47,250

11) -40·p·q÷(-2)² = -10·p·q

12) 0.003 × 0.045 = 1.35 × 10⁻⁴

13) N40°W = 320°

14) The base diameter of the cylinder = √(4 × (700×π cm³/7)/π) = 20 cm

15) The LCM of 2·x²·y, 3·x·y² is 12·x²·y²

16) 636,000 = 6.36 × 10⁵

17) 1/3·π·r²·h₁ = π·r²·h₂

h₂/h₁ = 1/3·π·r²/( π·r²) = 1/3

h₂/12 =  1/3

h₂ = 12/3 = 4 cm, the height of the cylinder = 4 cm

18) The angle = 180 + 45 = 225°

19) The total surface area = 22/7×14²/4 +  22/7 ×14 × 20 = 1034 cm²

20) The number is 58/2 = 29.

4 0
3 years ago
The graph of the function f(x) = (x + 2)(x + 6) is shown in the picture
tester [92]

Answer: The function is negative for all real values of x.where

x < -2.

Step-by-step explanation:

Because the values ​​-4 and -6 are less than -2 which is the basis of the statement highlighted as the right one.

6 0
2 years ago
A bottle of cranberry juice contains 32 fluid ounces and costs $2.56. What is the unit rate?
Tamiku [17]
Unit rate is (cost) per 1 unit
the unit is fluid oz
'per' is fraction
cost/1unit
so we do
2.56/32
divide completely
2.56/32=0.08/1
the unit rate is $0.08 per oz
6 0
3 years ago
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