In the 6/52 lottery game, a player picks six numbers from 1 to 52. How many different choices does the player have if repetition is not allowed? Note that the order of the numbers is not important.

The number of different choices the players have is 20,358,520.

Step-by-step explanation:

Combination can be used to solve this problem.

Combination is the selection of k objects from n distinct objects without replacement.

The cards available are numbered from 1 to 52,i.e. there are total 52 cards.

A player has to select 6 cards from these 52 cards.

Compute the number of ways to select 6 cards from the 52 cards as follows:

Thus, the number of different choices the players have is 20,358,520.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be