Question

Suppose a box contains a set of n balls (n >=4) (denoted by B) of four different colours
(may have different sizes), viz. red, blue, green and yellow. Show that a relation R de
fined on Bas R={(1,6); balls b, and b, have the same colour) is an equivalence relation
on B. How many equivalence classes can you find with respect to R?
[Note: On any set X a relation R={(x,y): x and y satisfy the same property P) is an
equivalence relation. As far as the property Pis concerned, elements x and y are deemed
equivalent. For different P we get different equivalence relations on X]​

Answer 1

Step-by-step explanation:

Four different-coloured balls are to be chosen at least one apiece in a sample size of 5.

So, in the sample size of 5, there will be two number of a particular coloured balls while three other coloured balls will be there one apiece.

So, the answer will be

= (4C2)*(5C1)*(6C1)*(7C1) + (4C1)*(5C2)*(6C1)*(7C1) + (4C1)*(5C1)*(6C2)*(7C1) + (4C1)*(5C1)*(6C1)*(7C2)

= 6*5*6*7 + 4*10*6*7 + 4*5*15*7 + 4*5*6*21

= 1260 + 1680 + 2100 + 2520

= 7560.