Question

@ganeishie8 say u have n number of 2s and 5s, how many ways to multiply these numbers together to give unique products

Answer 1

this problem came up because

Answer 2

say i got the number 1000s how many numbers would go into 1000

Answer 3

or 10000 and so on

Answer 4

\(2^n 5^n\)

Answer 5

hmmm

Answer 6

why do u say that

Answer 7

you want to take unique how many unique numbers we can construct from them ha ?

Answer 8

tell me how ur thinking about it

Answer 9

wHY AM I NOT THINKING ABOUT THISS RIIGHHT T_T!!

Answer 10

isnt it an easy question

Answer 11

say u got 3 boys and 3 girls, how many ways to load a bus with different combinations of boys and girls

Answer 12

where u can take any number of passengers 0 to 6

Answer 13

(3+1)(3+1)

Answer 14

right ?

Answer 15

yes it is 16

Answer 16

there are 0-3 ways for boy
and 0-3 ways for girl

Answer 17

sorry what do you mean

Answer 18

like we can pick either 0 or 1 or 2 or 3 girls

Answer 19

and we can pick 0 or 1 or 2 or 3 boys

Answer 20

oh wow ok i got it

Answer 21

say, the prime factorization for some number is : \(2^n 5^n\)b

Answer 22

yeah

Answer 23

there u have a total of (n+1)^2 factors

Answer 24

you wanto compute how many factors are there in it ?

Answer 25

is that right

Answer 26

in general,

if the prime factorization is \(\large p_1^{k_1} p_2^{k_2}p_3^{k_3}....\)

Answer 27

(k+1)(k2+1)(k3+1)...?

Answer 28

we can compute the number of divisors

Answer 29

yes :)

Answer 30

that gives number of positive divisors of a number

Answer 31

let me just think a little it make sense for the most part but

Answer 32

\(\large n= \large p_1^{k_1} p_2^{k_2}p_3^{k_3}....\)

Answer 33

we're kinda taking the fact that when we are choosing nothing, theres just a 1 in there by default