How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?

Options

A. 15
B. 13
C. 12
D. 11

Answer

D

Explanation

As `0 lt x lt 1`, we have `p lt q`
The number of rational numbers=5+4+3+2+1=15
When p,q have a common factor, we get some rational numbers which are not different from those already counted.
There are 4 such numbers `(2)/(4),(2)/(6),(3)/(6),(4)/(6)`.
`therefore` The required of rational numbers=15-4=11