UPSC CDS 2 2020 Math Paper

given that abc=30;a,b and c are positive integer
abc=30=1×1×30⇒ number of solution =

3!

2!

=3
abc=30=1×2×15⇒ number of solution =3!=6
abc=30=1×3×10⇒ number of solution =3!=6
abc=30=1×5×6⇒ number of solution =3!=6
abc=30=2×3×5⇒ number of solution =3!=6
Total number of solutions =3+6+6+6+6=27