In how many distinct ways can the product `xy^2z^2` be written without using exponents?

In how many lines two distinct planes can intersect?

In how many points two distinct lines can intersect?

In how many points two distinct planes can intersect?

In how many ways can the letters of the expressions x^(2)y^(3)z^(4) be arranged when written without using exponents?

There are 6 roads between A & B and 4 roads between B & C. (i) In how many ways can one drive from A to C by way of B? (ii) In how many ways can one drive from A to C and back to A, passing through B on both trips? (iiiI In how many ways can one drive the circular trip described in (ii) without using the same road more than once?

In how many ways can the letters of the word ALGEBRA be arranged without changing the relative order of the vowels and consonants?

In how many ways can 576 be expressed as the product of two distinct factors?

In how many ways can be letters of the word "MULTIPLE" be arranged without changing the order of the vowels in the word ?