How many positive integer factors of 100 factorial, are multiples of 2 or 3?

100 factorial is 1*2*3**100

Number of multiples of 2 less than 100 = 49

Number of multiples of 3 less than 100 = 33

We are double counting those that are multiples of 2 and 3 (or 6)

Number of multiples of 6 less than 100 = 16

49+33-16 =66

There are 66 factors that are multiples or 2 or 3

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.