How many different elements does A x B x C have if A has m e

How many different elements does A x B x C have if A has m elements, B has n elements, and C has p elements?

The number of elements in the AXB is given by (number of elements in A) * (number of elements in B)

Ex - A = (1.2) and B = (3,4,5)

AXB = { (1,3),(1,4),(1,5),(2,3),(2,4),(2,5)}, which is equal to 2X3 = 6 elements

Hence AXB contains mn elements

Now assuming D = AXB

then DXC will contain (number of elements in D) * (number of elements in C)

=> (number of elements in (AXB)) * (number of elements in C)

=> (m*n) * p

= (mnp)

Hence the number of different elements in A x B x C is equal to mnp elements