Astandard deck of 52 cards contains 13 cards with hearts, 13 with diamonds, 13 with clubs, and 13 with spades. how many 7-card hands are possible with 2 hearts, 2 diamonds, 2 clubs, and 1 spade? assume that the order of the cards does not matter, and use the formula for combinations to find your answer.

combinations.

Step-by-step explanation:

Given : A standard deck of 52 cards contains 13 cards with hearts, 13 with diamonds, 13 with clubs, and 13 with spades.

To find : The combination of 7-cards with 2 hearts, 2 diamonds, 2 clubs, and 1 spade.

Solution : Total 7 cards are in hand out of 52 cards in which,

2 hearts out of 13 hearts

2 diamonds out of 13 diamonds

2 clubs out of 13 clubs

1 spade out of 13 spades

As order doesn't matter,

Therefore the combination is

→

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15