Starc was not named in the playing XI for the third and final ODI against India.
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Starc, who struggled in the first two games of the ODI series, joined opener David Warner in the injury room.
“We have got three changes. Starc got a back and rib niggle and the medical team informed us that he will greatly benefit by resting, and obviously Davey and Pat Cummins not playing today,” Finch said at the toss.
“Green is making his debut, Sean Abbott and Ashton Agar come in too. Marnus will be opening for us. No such thing as a dead-rubber when you are playing for Australia and we will be doing everything we can to try and win the game,” he added.
Starc struggled for line and length in the first two ODIs as he claimed only one wicket by conceding 147 runs.
Having won the first two games, Australia have already clinched the ODI series.
The ODIs will be followed by three T20Is and four Tests.