I have 30 photos to post on my website. I’m planning to post these on two web pa

Question

I have 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.

Please 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 may ways can I post these photos to the web pages if the order in which the
photos appear on those pages does not matter?

Explanation / Answer

a) friends / family
30 / 0 : 30! / 0!
29 / 1 : 29! / 1!
28 / 2 : 28! / 2!
.......
........
3 / 27: 3! / 27!
2 / 28: 2! / 28!
1 / 29: 1! / 29!
0 / 30: 0! / 30!

total no of ways = 30! + 29! + 28! + 27! +26!+.........+3! + 2! + 1!

b) if the order doesn't matters

no of ways photos can be posted in either group =

friends / family
30 / 0 : 30 / 0
29 / 1 : 29 / 1
28 / 2 : 28 / 2
.......
........
3 / 27: 3 / 27
2 / 28: 2 / 28
1 / 29: 1 / 29
0 / 30: 0 / 30

     total no of ways = 0+1+2+3+.......+26+27+28+29+30

                              = 465

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.