Ihave 30 photos to post on my website. i'm planning to post these on two web pages, one marked "friends" and the other marked "family". no photo may go on both pages, but every photo will end up on one or the other. conceivably, one of the pages may be empty. answer these two questions:
a. in how many ways can i post these photos to the web pages if the order in which the photos appear on those pages matters?
b. in how many ways can i post these photos to the web pages if the order in which the photos appear on those pages does not matter?

a) 870

b) 435

Step-by-step explanation:

a)

number of photos to be posted =n = 30

number of web pages on which they would be posted is 2

Since the order in which the photos appear on the web pages matters,

Number of ways = 30 permutation 2

=870 ways

b)

Since the order in which the photos appear on the web pages does not matter,

Number of ways = 30 combination 2

= 435 ways

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.