yes the ans has to be 15.
explaination:
sinc we r getting 5 dark lines it means 5 excitation has occured.
1) n=1 to n=2
2)n=1 to n=3
3)n=1 to n=4
4)n=1 to n=5
5)n=1 to n=6
now these excited electrons come back in various ways to gv bright lines.
fst electron can in only one way that is n=2 to n=1 so we'll get one line
2) second w'll come in two ways n=3 to n=2 and n=3 to n=1 giving 2 lines
3) third w'll come in three ways n=4 to n=1 , n=4 to n=3 ,n=4 to n=1 giving 3 lines
4)fourth w'll come in four ways n=5 to n=1 ,n=5 to n=4, n=5 to n=3, n=5 to n=2
5) fifth w'll come in 5 ways n=6 to n=1,2,3,4,5 giving 5 lines
so total lines=1+2+3+4+5=15