In a container, a mixture is prepared by mixing of three samples of hydrogen, helium ion and lithium ion .In sample all the hydrogen atoms are in 1st excited state and all the He+ ions are in third excited state and all the Li2+ ions are in fifth excited state .Find the total number of spectral lines observed in the emission spectrum of such a sample when electrons return back upto to ground state.

H First excited state    He+ 3rd excited state    Li2+ 5th excited state
1.   2-1                           1.   4-1                        1.         6-1
                                  2.   4-2                        2.   6-2
                                       3.   4-3                        3.   6-3
                                  4.   3-1                        4.   6-4

                                  5.   3-2                        5.   6-5
                                  6.   2-1                        6.   5-1
                                                                   7.   5-2
                                                                   8.   5-3
total is 22                                                           9.   5-4
                                                                   10.   4-1
                                                                   11.   4-2
                                                                   12.   4-3
                                                                   13.   3-1
                                                                   14.   3-2
                                                                   15.   2-1
Electron jumps from excited energy level to lower energy levels and for every transition  it creates a line spectrum.

For example if it is in excited state  3 then it means it is in shell number 4 and electron can come to  energy level 3,2,1
Then from 3 energy level it can come to level number 2 and 1
From 2nd level to level 1

Similarly if electron is in 5th excited state of hydrogen atom then it means it is in level number 6
From 6th shell electron can come to shell 5,4,3,2,1
Then from  shell it can come to 4,3,2,1 and so on
You need to  identify all these energy transitions and add them together to know total number of lines in the spectrum.