Question

In a guidebook on Italy, you find 10 cities you wish to visit, but only have time on your upcoming trip to visit 6. How many unique itineraries are possible for you to choose?

Answer 1

Do any of you understand this? lol

Answer 2

i think n!An (refers to permutation maths)

Answer 3

I think your doing this correctly, cause im clueless lol

Answer 4

ok, as i understand it, if you just had 10 cities that you were visiting, and you wanted to know all the different orders you could visit them in (permutations), the answer would be 10! (10 factorial)
which is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
=3,628,800 different combinations / permutations for the order you could visit each
...this making sense so far?

Answer 5

yeah, this is making sense so far. I understand that part

Answer 6

10c6 is the answer dear..

Answer 7

oh, thanks

Answer 8

cool,
but in your question: we've got 10- cities to choose from, but you're only going to visit 6
so
10 x 9 x 8 x 7 x 6 x 5
=

Answer 9

that makes complete sense :P

Answer 10

hold on a sec

Answer 11

151200?

Answer 12

i think so, i got that answer (151200)
but @divu.mkr said 10c6, which is a binomial coefficient meaning 10! / (4! x 6!)
which = 210
...so maybe he's right?

Answer 13

probably?

Answer 14

what about 210? 151200 is so unusual

Answer 15

lmfao sounds better

Answer 16

ok... 151200 makes sense to me though
initially you have 10 to choose from
then 9
then 8
then 7... etc
after your 6th choice you finish.... i dunno it just seems logical

Answer 17

yeah, i'll try both eventually
but 151200 makes sense

Answer 18

sweeeet, good luck ;D

Answer 19

we have to chooses only 6..

Answer 20

big guns will settle this: @hartnn ??? please help dude?

Answer 21

ok, say the cities are named, one , to, three, ....ten

so, if unique itenary means the order IS NOT IMPORTANT, then we have \(^{10} C_6\) possibilities,
means (one, three, four.....)
and (one,four,three,...) are one and same


but if the order is important , means (one, three, four.....)
and (one,four,three,...) are different, then we have 10*9*8*7*6*5 possibilities

Answer 22

my guess the question meant the first option

Answer 23

ah ha, gotcha, cheers for that man hey!

Answer 24

and 10 C 6 was 210 combinations, yeah?

Answer 25

yes, correct

Answer 26

rockin, cheers man and thanks for clearin that up

Answer 27

welcome :)

Answer 28

i also gave that answer... :( @Jack1

Answer 29

aww... c'mon sulky, u didn't explain it tho, no brownie points for u ;D

Answer 30

hattttt :P main baat nahi karta :P