+0

# Counting #2

+1
286
16
+508

is it 46?

Jun 10, 2021

#9
+2403
+2

This has a really nice method.

B will be left of A 50% of the time, right of A 50% of the time.

5*4*3*2*1 total ways to be in a line, 50% of which are where B is on the left of A.

5*4*3*2*1/2 = 60

=^._.^=

Jun 10, 2021

#1
+201
+1

oops lemme recalculate

Jun 10, 2021
edited by mathisopandcool  Jun 10, 2021
#3
+201
+1

30 ways i can explain it but my working got deleted when i was writing it

mathisopandcool  Jun 10, 2021
#2
+508
+1

sure!

Jun 10, 2021
#4
+201
0

If B is adjacent to A we can make them as 1 letter, so  4!=24

If B is one away from A, we have 4 cases.

BDAC

DBCA

CBDA

If B is two away from A we get:

BCDA

BDCA

24+4+2=30

30 ways

Jun 10, 2021
#5
+201
0

wait sorry its wrong im dumb

mathisopandcool  Jun 10, 2021
#6
+201
0

there are 5 numbers not 4

Jun 10, 2021
#7
+201
0

You get 24

plus

9

plus

12

plus

6

24+9+12+6

33+18

51 im rlly bad at math idk if this is r

mathisopandcool  Jun 10, 2021
#8
+117766
0

Jun 10, 2021
#9
+2403
+2

This has a really nice method.

B will be left of A 50% of the time, right of A 50% of the time.

5*4*3*2*1 total ways to be in a line, 50% of which are where B is on the left of A.

5*4*3*2*1/2 = 60

=^._.^=

catmg Jun 10, 2021
#10
+117766
+1

That is a REALLY nice method catmg.  Thanks for showing it :)

Give yourself a point!

Melody  Jun 10, 2021
edited by Melody  Jun 10, 2021
#12
+2403
+1

Thank you. :))

=^._.^=

catmg  Jun 10, 2021
#11
+117766
+2

Lets have a look at your method mathisopandcool

XXXXB       4!             = 24

XXXBX       3*3!          =18

XXBXX       3*2! *2      =12

XBXXX      3!              =6

total = 24+18+12+6 = 60 ways

If you want me to explain any of these just ask.

Jun 10, 2021
#13
+36432
+3

A  X  X  X  X       Four ways for B to be to the right

X A X X X           Three ways

X X A X X            Two ways

X X X A X              One way     total of 10 ways

the other three slots can be filled in   3 * 2 *1   ways  = 6 ways for EACH of the 10 possibles

10 * 6 = 60 ways

Jun 10, 2021
#14
+117766
+1

That is a nice easy way too EP Thanks for showing us.

Your way is better than doing them all individually like in my demo.

Personally, I like catmgs way best but it is really good to see lots of alternative methods.

Melody  Jun 11, 2021
#15
+36432
+2

Agee!   catmg method  was pretty slick !

ElectricPavlov  Jun 11, 2021
#16
+508
+1

ok ok thanks for all the help!

Jun 11, 2021