Bhartiya sanvidhan ke anusar anuchchhed 75 ke tahat Bharat ka Rashtrapati hi Pradhanmantri ki Niyukti karta hai, parantu Rashtrapati Sidhe hi Pradhanmantri ki Niyukti nahin karta apitu vah Loksabha mein bahumat prapt Dal Ke Neta ko ya us Dal Ke Pramukh ko Pradhanmantri ke roop Mein niyukt karta hai aur Loksabha ka chunav vah Chunav Hota Hai jismein Janata Sidhe hi mahatvpurn bhagidari nibhati hai

Hello Pushkar,

The prime minister is selected by the members of lok sabha, rather than directly elected by the voters. The party or coalition holding majority in the lok Sabha elects its leader as prime minister.

After this , the appointment of prime minister is done by the president of India on the recommendation of the members of parliament.

Good luck,

Hope it helps :)