Astandard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all. how many 7-card hands will consist of exactly 2 hearts and 3 clubs?

1,977,300

Step-by-step explanation:

Given,

Total cards = 52,

In which,

Clubs = 13, diamond = 13, heart = 13, spades = 13,

Ways of choosing exactly 2 hearts =

Ways of choosing exactly 3 clubs =

So, the total possible ways of selecting 7 cards that contains exactly 2 hearts and 3 clubs

= Choosing exactly 2 hearts × Choosing exactly 3 clubs × choosing any 2 cards except hearts and clubs

= 1,977,300

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.