Diego's doctor has recommended that his daily diet should include 3 vegetables, 2 fruits, and 2 whole grains. At the grocery store, Diego has a choice of 9 vegetables, 9 fruits, and 11 whole grains. In how many ways can he get his daily requirements if he doesn't like to eat 2 servings of the same thing in 1 day

166320 ways

Step-by-step explanation:

In this case we must calculate the number of combinations for each option, and then multiply the result of each one, like this:

Number of ways you can choose 3 vegetables out of 9 available:

nCr = n! / (r! * (n-r)!)

in this case n = 9, r = 3, replacing:

9C3 = 9! / (3! * (9-3)!) = 84

Number of ways you can choose 2 fruits out of 9 available:

9C2 = 9! / (2! * (9-2)!) = 36

Number of ways you can choose 2 whole grains out of 11 available:

11C2 = 11! / (2! * (11-2)!) = 55

So according to the rule of the products how many ways you can choose the daily diet

84*36*55 = 166320

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕