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The Australians made 288 for five off their 50 overs after winning the toss and restricted India to 254 for nine.
The announcement comes hours before the start of the first one-day international of a three-match series against Australia starting Saturday in Sydney
"It's just an opportunity to see Alex play in a position he's done quite bit of now in Big Bash and one-day cricket," said fellow opener Finch
It is another blow for Marsh who was axed from the Test squad to play Sri Lanka, along with his brother Shaun.
The BCCI gives bonuses for major tournaments like the World Cup or Champions Trophy but extra payments for a bilateral series is rare.
"Keeping in mind the workload of the bowler, it was best felt to give him adequate rest ahead of the home series against Australia."
Australia skipper Tim Paine desperately looked for positives after his side's 2-1 Test series loss to India, but couldn’t find much of them.
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