In how many ways can a set with five element be partitioned into three blocks. 10 points if you manage to help

Question

Please show me the working

S(5,3)=3S(4,3)+S(4,2)
S(4,3)=3S(3,3)+S(3,2)
S(4,2)=2S(3,2)+S(3,1)
S(3,2)=2S(2,2)+S(2,1) = 2 + 1 = 3
S(4,2)=2(3)+1 = 7
S(4,3)= 3 + 3 = 6
S(5,3)=3(6)+7 = 25

can't understand the answer

Answer 1

The ! is called factorial and any positive integer factorial (written as n!) is
n! = n(n-1); therefore, Melissa is right, 5! /3! = 20

here is the long way how she did it
5x4 =20
20x3 = 60
60x2 = 120
120x1 =120

3x2 = 6
6x1= 6

120 / 6 = 20

Next reduce it to the simplest form like Melisa did.
five factorial divided by three factorial. 5! / 3! = 20

Answer 2

to find out how many ways 5 elements can be partitioned any number of ways, you would do 5! which is 5x4x3x2x1. Since you want to know how many ways you can partition them into three blocks, you would do 5!/3! which is 5x4 = 20.

Answer 3

if i have understood your question correctly(i am not too sure i have!)
it will be 5C3 ways combination of 5 things taking three at a time
using the property of combinations 5C3=5C2=5*4/1*2=10 ways

Answer 4

if you teach math, wouldn't you be annoyed to have people giving him the answers to his (i didn't look at the icon, it may be a her) homework? where does homework help stop, and doing someone's homework, for them, start? DO YOUR OWN HOMEWORK, LEST YOU END UP POOR, LIKE ME!